Preheat oven to 325°F and line tins with cupcake papers or spray with non stick cooking spray.
In a large bowl, stir together zucchini, eggs, sugar, oil and vanilla.
Add to zucchini mixture, flour, cocoa, baking soda, baking powder and salt. Spoon into tins and bake for 20-25 minutes (30-35 minutes for large cupcakes).
For the frosting, beat cream cheese and butter until creamy with no lumps. Add powdered sugar, cocoa powder and vanilla. Beat until creamy and smooth. Frost as desired.