I'd like to check the collocation of verbs.

#1 Mother will bake us some cake today.
#2 Mother will make us some cake today.

Can I use " bake" and " make" with "cake"? Both are OK?
If so, is the type of a cake different when I use "bake " and "make"?
Or do you use both words interchangeably?

One more question. Is "some cake " should be " a cake"?

Thank you.
'Bake' collocates with 'cake' much more frequently than 'make', but the two verbs do not indicate different kinds of cake.

I am not a cook. Are cheesecakes baked? If not, 'make' would be more appropriate in the case of cheesecakes.

'Some cake' should be 'a cake' here, because she is baking a countable object. Later, when she is offering pieces of cake around, she may say, 'would you like some cake?'