Ben misquotes Shakespeare's Hamlet Act 2 Scene 2 (6.48). The line he was going for was, "What's Hecuba to him, or he to Hecuba."
Jubal references Mr. A Square from Flatland: A Romance of Many Dimensions by Edwin Abbott (1884) (13.73).
The Laputian flapper system from Jonathan Swift's Gulliver's Travels (1726) is compared to executive assistants, secretaries, clerks, and golfing buddies of modern politicians (14.1-7).
Jubal calls the Martians an Apollonian culture and calls human culture Dionysian by comparison (21.210). These terms originated in Nietzsche's The Birth of Tragedy (1871). To put it very, very simply, Apollonian culture is based on reason, restraint, and harmony while Dionysian is its far wilder opposite.
Among Ben's many nicknames for Jill, the first is Florence Nightingale, a famous British nurse who served during the Crimean War (4.56).
The Latin phrase Karthago delenda est ("Carthage must be destroyed") is used as Ben's original home password (8.123).
Jubal sees Jill as crossing a personal Rubicon after taking Mike to his house. The Rubicon is a small river that was crossed by Julius Caesar and his army. It is significant because its crossing symbolized the start of Caesar's civil war with the Roman Republic. To this day, to cross a Rubicon means go beyond the point of return (10.82).
Jubal notes that the SS troops of his world are not political figures like the Praetorian Guard of the Roman Republic. The Praetorians were a very politically active military unit. For example, they took part in the assassination of Emperor Caligula and subsequently put Emperor Claudius on the throne (18.30). Emperors tended not to mess with the Praetorians for obvious reasons.
Jubal says that Mike's wealth is greater than Croesus's. Croesus was the king of Lydia in antiquity, and his name still stands for wealth even today (18.42).
Jubal alludes to a sterile Norte Dame laboratory (22.45). The laboratory did exist back in the late 40s / early 50s—it might still exist in some form today—and was filled with animals who lived their entire lives in sterile, microbe-free environments. The idea was to have test animals free of disease, so researchers could infect the animals with a disease later on and know exactly what the animal had, no variables. Wow. (Source.)
Jubal compares his sexual tastes to Nero's, a Roman emperor infamous for his hedonistic lifestyle (33.25). Nero has him beat.
Jubal notes the similarities of Mike's Church of All Worlds and the Oneida Colony (33.73). The Oneida Colony was a religious commune founded in the mid-19th century. They practiced shared communal property, a complex system of sexuality, and even a form of eugenics called stirpiculture.
Religious and Mythological References:
Jubal quotes from the Gloria Patri, a short Christian hymn (14.125).
Jubal references the Tree of Knowledge of Good and Evil (17.284) from Genesis. He notes that Mike has never tasted of its fruit (i.e., he's an innocent dude).
Mahmoud quotes from the Qu'ran when he says, "'And if ye mingle your affairs with theirs, then they are your brothers" (19.87). The quote comes from AL-BAQARA, the second book of the Qu'ran.
Mike reads a host of religious books while questing for the truth (29.92). Among the titles are The Golden Bough: A Study in Magic and Religion by Sir James George Frazer and The Book of the Law by Aleister Crowley.
Mike calls Jill "Cybele" and "Isis" and a bunch of other characters from mythology (31.120-125). Check out why in the "Character Clues" section.
Jubal references the sexual promiscuity of many mythological gods like Zeus and Isis (33.114).
Ben compares Mike to Prometheus, the Greek god who gave mankind fire and was punished severely by Zeus for it (35.106).
It is strongly suggested throughout the novel that Mike is a reincarnation of the Archangel Michael from Christian mythology.
Jubal requires the Mars movement from The Nine Planet Symphony to be played for Mike at the World Federation conference (19.125). This symphony does not exist, but there are two possible ways to explain its mention here. First, Heinlein may have made a mistake and meant The Planets, Op 32, a seven-movement orchestral suite (not symphony) composed by Gustav Holst. (It is seven movements instead of nine because Holst didn't compose an Earth movement and Pluto hadn't been discovered yet. Poor Pluto—went from not-a-planet to planet to not-a-planet all in about a century.) The other possibility is that Heinlein simply made up the symphony. This idea can be problematic, too, since symphonies usually consists of four movements—five at the most—not nine. Either way, check out Holst's The Planets—it's pretty phenomenal.
Jubal's favorite sculptor is Auguste Rodin. He was a French sculptor who lived from the 19th to the early 20th centuries. He is mentioned several times in the novel, like when Mike buys Jubal an exact replica of "She Who Used to Be the Beautiful Heaulmière" in Chapter 22.
Jubal wants to buy the "Little Mermaid" sculpture to use as a memorial for Mike's grave. The sculpture was carved by Edvard Eriksen and it currently resides in Denmark.