Using a serrated knife, trim tops of 8-inch round cakes to make level. Place four strips of parchment paper around perimeter of a serving plate or lazy Susan. Place first layer on cake plate. Spread frosting over first layer with a small offset spatula so it extends just beyond edges.
Place remaining layer on top, bottom side up. Gently sweep away any loose crumbs with a pastry brush. Using an offset spatula, cover top and sides with a thin layer of frosting (also use any of the excess frosting visible between the layers). Refrigerate until set, about 30 minutes.
Using an offset spatula, cover cake again with remaining frosting. Repeat process with 6-inch round cakes. Serve.