"The cat likes to eat mice."
Translation:Кошка любит есть мышей.
It's accusative, мыше́й is animate.
All plural nouns have almost the same declension regardless of the gender. Only singular feminine nouns have a separate accusative form.
The suggested answer has ко́шка, not ко́шке: Ко́шка лю́бит есть мыше́й 'Cat likes to-eat mice'. Ко́шка is the subject of the sentence, it does an action of 'liking' (it's not really an action but the language allows us to describe 'liking' as if it were some action done by cat).
You can use ко́шке if you use a different verb: «Ко́шке нра́вится есть мыше́й» 'To-cat it-is-appealing to-eat mice'. Here, the sentence is subjectless (in English, it has a dummy subject 'is'), so the action of the verb «нра́вится» is a state of environment: somehow liking to eat mice is not a cat's decision, it's a state of the things. Note we use the same structure for the weater («Хо́лодно» 'It-is cold', «Ко́шке хо́лодно» 'Cat feels cold; To-cat it-is cold').
In the second construction, 'cat' is not a subject: it has not chosen to 'like' eating mice, it's simply how things are. So, cat is not really 'doer' of the action, therefore we use the dative case and not the nominative in Russian. (But only with нра́вится. Люби́ть has a 'doer'! Probably because люби́ть is somehow stronger and implies that when you лю́бишь something, you show this by actually doing something.)