Are both "עוגות השוקולד" and "העוגות השוקולד" acceptable translations of "The chocolate cakes"?
No, "העוגות השוקולד" is grammatically incorrect. In spoken Hebrew many people actually say "העוגות שוקולד", but that's also incorrect.
Only the second word gets ה' הידיעה.
Notice the difference between a construct like עוגות שוקולד and a noun + adjective combination like עוגות קטנות. They behave differently on adding the definite article: עוגות השוקולד (and Walrosse is absolutely right, in spoken Hebrew most people, myself included, would say העוגות שוקולד which is incorrect but more socially acceptable), but העוגות הקטנות. Mixing these patterns does not work - העוגות השוקולד is unacceptable and so is עוגות הקטנות.
While the English here is grammatically correct, it's not the way it would be normally said. Even if there were many chocolate cakes, they would be treated in AE as a collectve noun: "The chocolate cake IS on the table".