Cream butter in a large mixing bowl; gradually add sugar, beating until light and fluffy. Add eggs, one at a time, beating well after each addition.
Combine flour, baking powder, and salt; add to creamed mixture alternately with milk, beginning and ending with flour mixture. Stir in vanilla.
Pour batter into 3 greased and floured 9-inch round cake pans. Bake at 350° for 25 minutes or until a wooden pick inserted in center comes out clean. Cool in pans 10 minutes; remove from pans, and cool completely.
Spread frosting between layers and on top and sides of cooled cake. Sprinkle top and sides of frosted cake with grated coconut, if desired.