One thing Cullen can't resist is throwing in a few classical allusions in his poem. He's going way back to Greek mythology and throwing Sisyphus and Tantalus in the mix, but why? We already know they're both symbols of never-ending struggle and play into the paradox of God creating a world full of suffering, but that's not all they're good for. Cullen references Greek mythology to reinforce his education and talent as a poet. Just like traditional white poets in the past made allusions to Greek myths in their poems, Cullen does the same as if to say, "See, I can do it, and I'm black." He's adopting the mode of traditional poets to prove a point, and he proves it well.
Lines 5-6: Greek reference numero uno. Cullen brings Tantalus into the poem as a classical reference to Greek culture and mythology. Of course, Tantalus' plight as a man who will be tortured by fruit that he's not allowed to eat (like a black poet who's not allowed to sing?) is consistent with the theme of the poem, but it's also an example of the speaker's intelligence. He's referencing Greek culture as an example of his own education and ability to write sonnets in the way that white poets did in the past. And this is another way the speaker gets his point across. He's showing us he can write just as well as a white poet, so surely, he deserves to be heard.
Lines 7-8: Greek reference numero dos. Cullen brings in Sisyphus, the guy forever rolling a large boulder uphill. Sweet, sounds like fun… or not. It's constant struggle, which may have been what it felt like to be a black poet in America when nobody respected black poets. But it's also another example of the speaker's intelligence. He references Greek mythology to show that's he educated, can replicate the methods of white poets from the past, and requires a certain amount of intelligence and attention on behalf of his reader. One of the poem's central themes is the plight of being a black poet in America, and this classical allusion is a display of his ability to "sing" just like the white poets in the past, which reinforces his marveling at why black poets weren't respected when they were clearly just as talented as the poets who came before them.