Put oven rack in center position and preheat oven to 350°F. Grease and flour bottoms and sides of three 6-inch cake pans.
Separate the eggs, and then putt the whites in one medium-sized bowl and the yolks in a separate one. Add half 1/2 cup of the sugar to each bowl. Beat the egg whites until they stiffen; beat the egg yolks until they are a thick, pale yellow. Carefully fold stiff egg whites into egg yolks.
Whisk the flour into the egg, stirring in the butter, and then separate the batter into three bowls. Dye one red, one blue, and leave the third plain.
Pour batter into the cake pans and bake 12 to 18 minutes.
Let the cake cool in the pans for another 10-15 minutes, then remove to cool completely outside the oven. When room temperature, cool in refrigerator 20 minutes.
Then make your frosting! Cream butter until smooth. Add 3 cups confectioner’s sugar and continue beating.
Scrape sides of the bowl, and add vanilla. Add remaining sugar until it reaches desired consistency. If it gets too thick, add some milk.
Slice the white and red cakes horizontally to form stripes for the flag.
Frost the top of a red layer lightly, and place a white later atop it. LIghtly frost.
Repeat the above step as necessary until complete.
Cut a circle out of the center of the blue cake, and place circle layer on top of the rest of the cake.
Frost entire cake as desired, and place in refrigerator.