"They eat the cake."
Translation:Αυτοί τρώνε το κέικ.
Did I not take something into account?
The thing that gets eaten is the direct object of the verb "to eat", so it has to be in the accusative case, not nominative.
For neuter words, the accusative looks like the nominative, but other genders have different forms -- so you can't use nominative η τούρτα but would have to use accusative την τούρτα.