Can we use "not either" instead of "neither"?

Can we use "not either" instead of "neither"?

For example, given that…

  1. I don't like football
  2. I don't like basketball

… which of the following are correct?

A. I like neither football nor basketball.

B. I don't like either football or basketball.


Note: you cannot say "I like not either football not or basketball"; that sentence is incorrect.

You can however say:

I do not like football or basketball.