Divide 2/3 of the cake batter between 2 of the pans.
To the remaining 1/3 of the cake batter, add the cocoa powder (it's helpful to sift the cocoa powder over the cake batter and then whisk it in, to avoid lumps). Add a few drops of red gel food coloring, until you have your desired shade of red. Pour the red batter into the 3rd cake pan.
Bake on the center oven rack for about 25-30 minutes, until a cake tester or toothpick comes out clean. Set the pans on a wire rack, cover loosely with a clean kitchen towel, and cool completely before frosting.
Buttercream & Assembly
Prepare the American Buttercream as instructed: you'll need to make 4x the recipe to have enough to frost a 3-layer cake. For a bright white buttercream, substitute shortening for 1/2 of the butter in the recipe.
Remove the cooled cakes from the cake pans, and place one of the white cakes on a cake board. Frost with a layer of buttercream.
Add the red cake layer next, frost with a layer of buttercream, and top with the other white cake, so that the red is sandwiched between two layers of white.
Frost the cake all over with a thin crumb coat of buttercream. Chill in the refrigerator for 30 minutes.
Frost the cake with a final pretty coat of buttercream. You can make it smooth or swirly, whatever you like. Chill in the refrigerator for 30 minutes.
Take the remaining buttercream (you'll only need 1/2 cup) and tint it red with the red food coloring. Fit a piping bag with a coupler and tip #3; fill with the red buttercream.