Separate eggs. Allow egg yolks, egg whites, and butter to stand at room temperature for 30 minutes. Meanwhile, grease and lightly flour three 8x1-1/2-inch or 9x1-1/2-inch round cake pans; set pans aside. In a bowl, stir together flour and baking soda; set aside.
Preheat oven to 350 degrees F. In a very large mixing bowl, beat butter and shortening with an electric mixer on medium to high speed for 30 seconds. Add sugar; beat until well combined. Add the egg yolks and vanilla; beat on medium speed until combined. Alternately add flour mixture and buttermilk to butter mixture, beating on low speed after each addition just until combined. Fold in coconut and the 1/2 cup finely chopped pecans.
Thoroughly wash the beaters. In a mixing bowl beat egg whites until stiff peaks form (tips stand straight). Fold about one-third of the egg whites into cake batter to lighten. Fold in remaining whites. Spread batter evenly into the prepared pans.
Bake about 25 minutes for 9-inch pans, about 35 minutes for 8-inch pans, or until a wooden toothpick inserted near centers comes out clean. Cool cake layers in pans on wire racks for 10 minutes. Remove cake layers from pans. Cool thoroughly on wire racks.
Place one cake layer, bottom side up, on serving plate. Spread with about 1/2 cup of the Cream Cheese Frosting; sprinkle with 1/4 cup pecans. Top with second cake layer, bottom side down. Spread with 1/2 cup more frosting and sprinkle with 1/4 cup nuts. Top with remaining layer, bottom side up; spread top and sides of cake with remaining frosting. Press remaining nuts around side and on top of cake.**
Cream Cheese Frosting
In a mixing bowl, beat cream cheese, butter; and vanilla with an electric mixer on medium speed until light and fluffy. Gradually beat in 5-1/2 to 6 cups powdered sugar until well combined and a spreading consistency.