The White Devil Allusions & Cultural References

Literary and Philosophical References:

Democritus (1.1)

Lodovico references the "gods" of the Greek philosopher Democritus. This might be an ironic joke—Democritus apparently didn't deny the gods (although he said they weren't immortal), but was focused on the idea that everything was caused by the motions of atoms, as opposed to the will of the gods. Lodovico might be claiming that we live in a universe without a guiding intelligence, denying the existence of God or gods.
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Aristotle (1.2)

When trying to convince Camillo that he won't be cuckolded (even though Flamineo wants him to and knows he will be), Flamineo tells him to remember Aristotle's wisdom. Aristotle is typically considered to be one of the greatest Greek philosophers, along with Plato and Socrates.
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Ephemerides (1.2)

Flamineo also tells Camillo to remember Ephemerides—a famous Greek expert on astrology—and how Camillo was born under a favorable planet. Cmillo replies that he might be cuckolded during the day, when his favorable stars and planets aren't visible in the sky.
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Snow of Ida (1.2)

Flamineo mocks sonnet writers who would make crazy exaggerated comparison between the whiteness of a woman's cheek and the snows of Ida—a famous and sacred mountain in Crete where the god Zeus was nursed as a baby.
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Ivory of Corinth (1.2)

This is another high-flown sonnet comparison (on the same subject as the snows of Ida—a woman's cheek), which Flamineo mocks. Corinth was a famous Greek center of trade, wealth, and culture.
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Apples of Sodom (3.2)

Monticelso compares Vittoria to the "apples of Sodom"—an actual fruit that (according to legend) grows where the original Sin City—Sodom—used to be. In the Bible, God destroys Sodom for committing a variety of sins (mainly inhospitality). But the apples aren't really apples—they're green globes full of a gross, gray, bitter sap. (The sap, because of its grayness, is compared to ashes.) They're used as a metaphor for something that seems nice on the outside, but is corrupted within.
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Perseus (3.2)

Vittoria says that, in order to defend herself and deal with the harsh sentence Monticelso will probably give her, she will need to "personate masculine virtue" and act like Perseus—one of the most famous heroes of Greek mythology (the guy who killed the Medusa).

Cain and Abel (3.3), (5.6)

Flamineo says that "the first bloodshed in the world happened about religion"—which might be a reference to Cain murdering Abel, since God accepted Abel's sacrifice but not Cain's (thus causing Cain's jealousy and anger). After Flamineo murders his own brother, Marcello, Vittoria compares him to Cain, as well.

Polyphemus and Ulysses (4.2)

In The Odyssey, Polyphemus is a Cyclops who eats Odysseus' (Ulysses) sailors—saving Odysseus for last. (Fortunately, Odysseus blinds the Cyclops before he can eat him.) In The White Devil, Flamineo compares himself to Odysseus and Brachiano to Polyphemus, at one point, suggesting Brachiano will kill him when he's done killing his enemies—since Flamineo knows too much.

Slaughtered Sons of Dipus (Oedipus) (5.1)

Marcello compares himself and Flamineo to the sons of Oedipus—who both ended up fighting against each other to rule the city of Thebes, after their father died. They fought each other in man-to-man combat during the battle, and finally killed each other at the same time.
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The Furies (2.1), (4.2), (4.3), (5.6)

The furies were Greek goddesses of vengeance, who lived in the underworld. They would attack and destroy people who broke their oaths or generally needed punishment. They're referenced multiple times in the The White Devil—for instance, Lodovico uses them to describe the evil passions hidden inside Monticelso's heart.

Lethe (4.3)

When Brachiano gets over his jealousy, and decides to believe Vittoria wasn't going to cheat on him with Francisco, he says that he has drunk "Lethe"—Lethe being a river in the underworld in Greek mythology, where the souls of the dead would drink in order to forget their earthly lives.
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Styx (5.6)

After Vittoria breaks her promise to kill herself and tries to murder him, Flamineo says that breaking this kind of oath is terrible because it was an oath about death—the gods, in Greek myth, would never swear on the river Styx (the river between the underworld and the living world) for this reason.
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Machiavelli (5.3)

Machiavelli was a famous Italian philosopher from the 15th and 16th Centuries, known for such worldly-wise and cynical quotes as, "It is better to be feared than to be loved, if you cannot be both." When Brachiano is poisoned, Flamineo says that this is one of the "rare tricks of a Machiavellian"—which is ironic, since Flamineo and Brachiano are both super-Machiavellians.

Anacharsis (5.4)

Anacharsis was a figure in Greek philosophy known for being a wise "barbarian" (a person from Scythia). Flamineo says he doesn't care if he dies like Anacharsis, by being "pounded to death in a mortar." (Apparently, Anacharsis' own brother, who didn't approve of his new-fangled Greek habits and ways, murdered him.)
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Lucian (5.6)

Lucian was a Greek writer of satires. One of his most famous works Dialogues of the Dead is a series of imaginary conversations between famous people in the underworld. Flamineo references this when he pretends to die after Vittoria "shoots" him.
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World Leaders Past (5.6)

Flamineo references a ton of dead world leaders from Lucian's satire, as he fake-dies: 

"O Lucian, thy ridiculous purgatory! to
find Alexander the Great cobbling shoes, Pompey tagging points, and
Julius Cæsar making hair-buttons, Hannibal selling blacking, and
Augustus crying garlic, Charlemagne selling lists by the dozen, and
King Pepin crying apples in a cart drawn with one horse!" (5.6)

Hypermnestra (5.6)

Flamineo compares Vittoria unfavorably to Hypermnestra—a woman from Greek mythology who refused follow her father's orders, and murder her husband (unlike her forty-nine sisters, who did).
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Historical References

Vittoria Accoramboni

Vittoria Accoramboni (Corombona in the play) was a real figure, and her life story isn't all that different from the Vittoria in Webster's play—though some of the details are actually more brutal in the historical record. (However, Flamineo is an invention, or differently named version of Vittoria's brother. Vittoria's real-life bad-boy brother was named Marcello—although Webster's "Marcello" is a good guy.)

Pope Paul IV… Or, actually, Pope Sixtus V

In Webster's play, Cardinal Monticelso becomes Pope Paul IV—but Webster mixed popes up. The real basis for this character, Cardinal Montalto, actually became Pope Sixtus V (Pope Paul IV was just before him).

Lycurgus (1.2)

Lycrugus was a great Spartan lawgiver. According to Flamineo, he wondered why men spent so much time breeding horses, but not impregnating their own wives.

Tennis (or, Real Tennis) (2.1), (5.1)

Webster mentions "tennis" a bunch in The White Devil—but this is an older, though similar version of the game, now called "Real Tennis" (different from normal, popular Tennis).

"Shaved Polack" (2.1) and "Forty Thousand Pedlars in Poland" (3.3)

Brachiano makes a derogatory reference to a "shaved Polack"—at the time, Poles supposedly shaved all of their heads except for the forehead. Also, Flamineo mentions the "forty thousand pedlars [sic] in Poland"—since Poland was considered an impoverished backwater by English people at the time.

"Hemlock in thy Breath" (2.1)

Famously, Socrates died by drinking hemlock poison (as a death sentence). Brachiano tells Francisco he smells "hemlock in thy breath" when Francisco calls Vittoria a "strumpet."

Wolner

Flamineo cryptically tells Marcello to "practice the art of Wolner and swallow all that's given thee" and be able to throw it all up and get hungry again (maybe meaning to get over guilt quickly). Wolner was a famous English guy from Queen Elizabeth's time who could eat iron, glass, raw meat, etc.

"The Wild Irish" (4.1), (5.2)

Webster routinely references the Irish as being wild and rebellious, and as playing football with people's heads. This is because Ireland was constantly trying to regain its independence from England during Webster's lifetime, fighting in numerous rebellions.

Russians Breaking Shins (4.2)

After Brachiano threatens to kick Flamineo, Flamineo says that he's not Russian and has the right to keep his shins intact. At the time, debtors in Russia were punished with shin-breaking.

Lions in the Tower on Candlemas Day

Lions and other animals were kept in the Tower of London (the lions potentially being used for lion-baiting). Cryptically, on the verge of death, Flamineo tells people to be like the animals trapped in the tower (since, we're all ferocious spirits trapped in a nightmarish world), and fear the remainder of winter if Candlemas day is sunny. Candlemas Day is the same as Groundhog Day—if it's nice (and if the Groundhog can see his shadow) there's supposed to be six more weeks of winter. (Candlemas Day is also the day that the baby Jesus was, according to tradition, presented at the Temple in Jerusalem).