Cream butter; gradually add sugar, beating well.
Combine flour and baking powder; add to creamed mixture alternately with milk, beginning and ending with flour mixture. Mix well after each addition. Beat egg whites (at room temperature) until stiff peaks form; fold into batter.
Pour batter into 3 greased and floured 9-inch round cake pans. Bake at 375° for 15 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 sprinkle each with, 3/4 cup grated coconut. Spread remaining frosting on top and sides of cake and sprinkle with remaining coconut. Refrigerate until serving time.