Preheat oven to 325 degrees F. Line twenty-four muffin cups with liners and lightly coat with nonstick cooking spray; set aside.
In a large bowl stir together zucchini, eggs, sugar, oil, and vanilla.
Add flour, cocoa powder, baking soda, salt, baking powder and stir until combined.
Using a large ice cream scoop, scoop batter into prepared pans, filling cups about half full.
Bake about 25 minutes or until a wooden toothpick inserted near centers comes out clean.
Cool in muffin pan on wire racks for 5 minutes.
Remove muffins from muffin pan and cool completely on racks.
After cupcakes have cooled, make the Cream Cheese Frosting.
In large bowl, using a mixer, beat together the cream cheese and butter until creamy.
Add powdered sugar and vanilla.
Continue beating until smooth and creamy. Frosts 20 - 24 cupcakes.