Hi, Both are correct and mean the same thing. There is no cake left. — more direct and neutral. There isn’t any cake left. — slightly more conversational or soft.

Both are correct, but in the first case I'd contract there + is = there's There's no cake left!

both are correct. As a Native English speaker from the States, it is more common for me to hear and say either number two or take number one and modify it to "there's no cake left"

Both, 1. colloquial 2. standard