Preheat the oven to 350 degrees F (175 degrees C). Lightly grease a 9x13-inch baking pan.
Mix white cake mix, 2 eggs, and 1/2 cup oil together in a bowl. Press mixture into the prepared baking pan.
Bake in the preheated oven until just set, about 10 minutes. Leave oven on.
Mix red velvet cake mix, 2 eggs, and 1/2 cup oil together in a bowl. Press mixture carefully on top of the first cake layer in the baking pan.
Bake in the hot oven until a toothpick inserted into the middle comes out clean, about 20 minutes more. Let cool completely, about 30 minutes. Spread a layer of cream cheese frosting on top and cut into bars.