Preheat your oven to 350 degrees. Prepare three 9 inch round cake pans by cutting a circle of parchment paper for the bottom, and spraying the edges. Set aside. (See directions in the post for making this into a sheet cake.)
Whisk together in a large bowl the flour, cocoa powder, baking powder, baking soda, and spices.
Whisk the eggs and sugars together in a large bowl until the sugars are just about dissolved. Now add the oil about a half a cup at a time and whisk in until it’s combined.
Slowly add the flour mixture. Stir in the zucchini (Learn more about zucchini in baking in the post). Pour into the cake pans and bake for 20 to 25 minutes or until a toothpick inserted into the center of the pan comes out clean. Allow to cool completely. Beat together the butter and cream cheese. Add in the powdered sugar and the vanilla. Beat until smooth. (Learn more about making cream cheese frosting in the post.)
When assembling the cake, add about 3/4 cup of frosting to the top of the first cake layer, spreading it out evenly. Top it with the second layer and add another 3/4 cup of frosting to that layer. Add the final layer and then spread the remaining frosting out over the whole cake. Slice and enjoy.