"He is eating cake."
Translation:Er isst Kuchen.
Just to confirm: no article because the same word for both singular and plural?
This is called "Nullartikel". It is used, among other things, when refering to uncountable nouns or an undefined number of countable nouns.
Kuchen is a special case, as it can be considered countable or uncountable. So this sentence could mean "He eats some (amount of) cake" (uncountable) or "He eats (an unknown number of) cakes (countable).
It also works with other words
Er isst Äpfel - He eats apples (countable but undefined)
Er trinkt Wasser - He drinks water (uncountable)