this is cake

[Unregistered]

I show my friend a picture of a cake

Which is the most natural sentence?

This is a cake
This is cake

I like birthday cakes
I like birthday cake

[tedtmc]

This is a cake
I like birthday cakes

[David L.]

This is a cake
The picture would show a whole cake, whether a large cake to be cut, or a small individual cake.

This is cake
You might say this to the dry-cleaner when you take in a piece of clothing, to indicate the nature of some greasy (cream), reddish (jam or icing) stain, so he knows how to remove it. Or a stain on the carpet after the party!
Another way might be if somebody totally new to English really didn't know the difference between biscuits and cake, and you showed them a picture of each, and pointed to it and said, "This is cake." Usually, if it was a slice of cake, that is how we would refer to it:" "this is a slice of cake", "This is a piece of cake", rather than just, "This is cake."

I like birthday cakes
Talking about the look of birthday cakes in general, the decoration of them etc

I like birthday cake
You like the taste!

[BobK]

David's 'a piece of cake' reminds me of an interesting idiom (maybe just Br Eng). Something (anything) that's very easy is 'a piece of cake'; sometimes we use 'it's a cinch' with the same meaning; but as that idiom was born in America, referring to the last thing you did before mounting a horse, I suspect that in Am English it may mean something more like 'I'm ready to go' Does it?

Example: 'The exam was a piece of cake/a cinch.' (As I say, this may only apply to Br Eng).

b