Preheat oven to 350 degrees. Cream butter and shortening. Add sugar and beat well. Add egg yolks and beat well again. Sift flour and soda. Add to creamed mixture, alternating with milk. Stir in vanilla, coconut, and pecans. Fold in egg whites. Place batter in 3-9", greased and floured pans. Bake for approximately 25 minutes.
Cream together butter and cream cheese. Add powdered sugar and beat well. Add vanilla and nuts, stir well. After cake is cooled well, frost bottom layer, add 2nd layer, frost and repeat with 3rd layer, making sure you spread icing all over the top and sides of the cake.
TIP: To keep cake moist, keep in refridgrator until ready to serve.