Preheat the oven to 325°F. Lightly grease and flour your choice of pans: one 9" x 13" pan, two 9" round pans, or three 8" round pans.
Sift together the flour, baking powder, baking soda, salt, cocoa, and sugar into a large mixing bowl.
Add the butter and mix at low speed for 1 minute. With the mixer running, add the oil and continue mixing until the mixture looks sandy, about 30 seconds more.
In a separate bowl, combine the vanilla with the milk and coffee, and add all at once to the dry ingredients. Mix for 1 minute at low speed, stopping to scrape the sides and bottom of the bowl, then mix for 30 seconds more.
Add the eggs one at a time, beating well at medium-high speed between additions.
Scrape the sides and bottom of the mixing bowl, and mix for 30 seconds more. The batter will be thin.
Transfer the batter to the prepared pan(s) of your choice. Smooth out the tops of the layers with an offset spatula.
Bake for 34 minutes for a 9″ x 13″ pan, 28 to 30 minutes for 9″ layers, and 24 to 26 minutes for 8″ layers.
The cake is done when the top springs back when very lightly touched in the center, and the edges just begin to pull away from the edge of the pan. A cake tester inserted in the center will come out clean.
Remove the cake from the oven and let cool completely in the pan(s) on a rack before turning out of the pans to frost.