Notice, theprofessor told the class, Cassius' choice of imagery when he asks, upon what meat doth this our Caesar feed that he is grown so great?
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This is the correct punctuation for quotes and quotes within quotes in the U.S. If you're in the U.K., the punctuation is different.
"Notice," the professor told the class, "Cassius' choice of imagery when he asks, 'Upon what meat doth our Caesar feed that he is grown so great?'"