Is cake a common or proper noun?

The Word 'bakes' is not a noun; the Word 'bakes' is the present tense for the verb 'to bake' (bakes, baking, baked).

The noun form 'bake', as in clam bake, is a common noun.

Noun forms for the verb 'to bake' are 'baker', one who bakes, a common noun; and the verbal noun (gerund), 'baking', also a common noun.