Grammatically, the third one is much more reasonable which means :"you can't eat your cake, and you can't have it either ("neither" here is also OK for me) ". "either" here works as an adverb which show that a negative statement is also true. I am not good at English myself, you know, I am just trying to help which means my explanation maybe not correct.
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northwindYou can't eat your cake and have it.
You can't eat your cake and have it too.
You can't eat your cake and have it either.
I think the first and the sencond sentences are correct and the first sentence could have the same meaning as the second.
I can't judge the third sentence. It's so tough.
You're okay. "Too" m