Preheat the oven to 350 degrees. Butter and flour a 9-by-13-inch jelly roll or cake pan.
In a large bowl, whisk together the sugars, baking powder, and flour. Set aside.
In a medium saucepan, combine the Coca-Cola, butter, oil, and cocoa and bring to a boil over medium heat. Allow to cool slightly.
Beat into dry ingredients.
Stir in the eggs, milk, and vanilla.
Pour into prepared pan.
Bake until a toothpick inserted in the center comes out clean, 35 to 45 minutes. Cool, in pan, on a wire rack for 5 minutes then remove from pan and continue to cool on a wire rack.