Beat egg whites at high speed with an electric mixer until stiff peaks form; set aside.
Beat butter and shortening until creamy; gradually add sugar, beating well. Add egg yolks, 1 at a time, beating until blended after each addition.
Combine flour, cocoa, and baking 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, chopped pecans, and vanilla. Fold in egg whites. Pour batter into 3 greased and floured 8-inch round cakepans.
Bake at 325° for 25 to 30 minutes or until a wooden pick inserted in center comes out clean. Cool in pans 10 minutes. Remove cake layers to wire racks, and cool completely.
Spread Chocolate-Cream Cheese Frosting between layers and on top and sides of cake. Garnish, if desired.