Yes. "Seven Minute Frosting" is made with ordinary granulated sugar. See link for recipe. Probably better to make your way to the store and invest in a can of frosting--or forgo the frosting...
Cream together 1/2 cup butter, 1/2 cup shortening, 1 cup of white sugar and some vanilla for taste. Then scald 3/4 cup milk and cool until lukewarm...then slowly whip in to your cream mixture until...