Preheat the oven to 350F (180C). Line the bottom of the round cake pans with parchment paper and grease the sides. If using a 9x13 inch pan, grease and dust with cocoa powder.
Wash the zucchini. Slice off the ends and grate using a cheese grater. If the strands are long, chop them so that they are about 1 inch in length (you don't need to be exact with this). Blot with a paper towel so that the zucchini isn't dripping wet. Set aside.
In a very large bowl, sift together the flour, cocoa, baking powder, baking soda and salt so that there are no lumps. Add in the granulated sugar. Whisk for about 15-20 seconds until evenly combined. Set aside.
In a large bowl, whisk together the melted butter, oil, brown sugar, eggs, sour cream, vanilla extract and instant espresso powder (optional but recommended). Whisk until you no longer see pieces of egg or lumps of brown sugar.
Make a well in the middle of the dry ingredients and pour the wet ingredients into the well. Gently fold together using a rubber spatula or wooden spoon. Do a few stirs until the mixture looks about 50% combined (you will still see lumps and streaks of dry ingredients.
Add the grated zucchini to the batter. Do a few more stirs by hand, then mix with an electric mixer until you no longer see streaks or lumps of dry ingredients. The batter will be thick. You can do this entirely by hand answell.
Pour the batter into the prepared pans. Bake in the preheated oven for 40-45 minutes for two 8-inch round pans (with 2-inch sides). When the cakes are done baking the top should be set, the sides should be pulling away from the pan, and an inserted toothpick should come out clean. If you're unsure, I recommend baking for a few extra minutes - as this cake is very unlikely to dry out.
Cool the cakes fully. If making a layer cake, cool the cakes in the pans for at least 25 minutes, then carefully invert the pans and continue cooling on a wire rack. If using a 9x13 inch pan, cool the cake in the pan.