Bake your cakes, using about 25 drops of food coloring for the red cakes and about 20 for the blue cake. Let them cool in their pans for 15 minutes, then invert them onto a wire rack to cool completely.
While they cool, make your frosting: In the bowl of an electric mixer fitted with the paddle attachment, cream the butter and sugar until they’re light and fluffy, about 5 to 6 minutes. Beat in the vanilla, then add the cream gradually, mixing until you get a smooth, creamy texture.
Cut the red and white cakes into layers about 3/4 inch thick. You’ll want six layers total: three red, and three white. (Leave the blue layer whole — it has to be thicker to represent the square on the flag.)
Using a 4-inch round cookie cutter (or a paring knife to trace around a small plate or bowl that’s roughly 4 inches in diameter), cut one of the red layers into a smaller circle. Then do the same with one of the white layers. These small circles will be the shorter stripes that line up with the flag’s blue square. (You won’t need the outer rings for the cake, but save them to munch on!)
Then, use the same technique to cut a hole in the center of the blue cake. You won’t need the inner blue circle, so set it aside.
To build the cake, start with a red layer and top it with a thin coating of frosting. The key is to make it thin, otherwise you will interrupt the “stripe” effect. Top the red layer with a layer of white cake and another thin coating of frosting.
Repeat with another red layer and another white layer so that you have four layers total.
On top of this, place the blue cake doughnut (the thick layer with a hole in the middle).
Spread a thin layer of frosting onto the small red circle, and insert it into the hole of the blue cake. Top w/frosting and the small