"What kind of cake" would be better than "what cake." In the latter sense in referring to a choice among many available cakes 哪个 would be better
In English we do not need to specify "to eat" unlike in Mandarin. The English should be correct without having to add "to eat"
Does this sentence mean "which cake" or "what kind of cake"?
"what kind of cake do you want" should be right. god
"What cake do you like to eat". Would be accept.
想 expresses desire, so it's about wanting to eat, not liking.
"Would you like..." means wanting/ desiring = 想
" - not the same as liking.