"It can be countable or uncountable. When used as a countable noun, it means cake, such as: a birthday cake, a meat pie, and when used as an uncountable noun, it means fast and cake-like, such as: a of soap. They shared the birthday cake.

They share the birthday cake.

Finally, we ate the birthday cake.

Finally, we ate a birthday cake.

Mother is icing my birthday cake.

Mother is icing my birthday cake.

I want a delicious birthday cake.

I want a delicious birthday cake.

He made a birthday cake.

He made a birthday cake.

I want a birthday cake.

I want a birthday cake.