Preheat oven to 180 degrees C. Grease and flour a 22x33cm baking tin. Sift together the flour, baking powder, bicarb soda, salt, cinnamon and cocoa powder. Set aside.
In a large bowl, cream together the butter, oil and sugar until light and fluffy. Beat in the eggs one at a time then stir in the vanilla. In a small bowl, combine grated zucchini with milk. Beat in the flour mixture alternately with the zucchini mixture. Pour batter into prepared pan.
Bake in the preheated oven for 55 to 60 minutes, or until a skewer inserted into the centre of the cake comes out clean. Allow to cool.