In the sentence John ate the cake, the verb phrase is?

Verb means the action of the sentence, the action going on is 'ate', so that is the verb.

The verb phrase of the sentence is "ate the cake"

Explanation:

A verb phrase refers to the part or portion of a sentence that contains the verb and the object which can be either a direct or an indirect object.

Bearing this in mind, in the particular sentence provided John ate the cake, the verb phrase is "ate the cake" since ate corresponds to the verb and the cake corresponds to the direct object.