Beat butter and shortening at medium speed with an electric mixer until fluffy; gradually add sugar, beating well. Add egg yolks, 1 at a time, beating until blended after each addition. Add vanilla, beating until blended.
Combine flour and soda; add to butter mixture alternately with buttermilk, beginning and ending with flour mixture. Beat at low speed until blended after each addition. Stir in coconut.
Beat egg whites until stiff peaks form, and fold into batter. Pour batter into 3 greased and floured 9-inch round cakepans.
Bake at 350° for 25 minutes or until a wooden pick inserted in center comes out clean. Cool in pans on wire racks 10 minutes; remove from pans, and cool completely on wire racks.
Spread Nutty Cream Cheese Frosting between layers and on top and sides of cake. Garnish, if desired.