"Do you have any more cake?"
Translation:Onko sinulla lisää kakkua?
I said the same thing, and I reported it as should be correct, because in English, the questions:
"Do you have any more cake?" and "Do you have any cake left?"
Are closer in meaning to each other than to the question:
"Do you have more cake?" (without "any")
"Any more" means "any left," or "any remaining."
"More" by itself, as opposed to "any more," means more, beyond what was available to start with. Like, this cake is finished, but do you have another one hidden somewhere?