To prepare cake, coat a 12-cup Bundt pan with cooking spray.
Place sugars, cream cheese, and vegetable oil in a large bowl, and beat with a mixer at medium speed until well blended. Add eggs and beat in 1 teaspoon vanilla extract.
Combine 2 1/2 cups flour, 1/2 cup of cocoa, baking powder, baking soda, salt, and cinnamon in a medium bowl, stirring well with a whisk.
Add flour mixture and buttermilk. Stir in zucchini, and 2/3 cup chocolate chips. Pour batter into prepared pan. Bake at 350° for 1 hour or until a wooden pick inserted in cake comes out clean. Cool in pan 10 minutes on a wire rack; remove from pan. Cool completely on wire rack.