Preheat the oven to 350 degrees F (175 degrees C). Grease and flour three 9-inch round cake pans.

Blend cake mix, pudding mix, water, eggs, and oil in a large mixing bowl. Beat at medium speed for 4 minutes. Stir in 2 cups of coconut and chopped walnuts. Pour the batter into the prepared pans.

Bake in the preheated oven for 35 minutes. Let cakes cool in the pans for 15 minutes, then remove and finish cooling on a rack.

To Make Frosting: Melt 2 tablespoons butter in a skillet. Add 2 cups flaked coconut and stir constantly over low heat until golden brown. Spread coconut on absorbent paper to cool.

Cream remaining 2 tablespoons butter with cream cheese. Add milk and confectioners' sugar alternately, beating well. Add vanilla and stir in 1 3/4 cups toasted coconut.

To Assemble Cake: Spread tops of cooled cake layers with some of the frosting. Stack them and then frost the sides of the cake. Sprinkle cake with remaining toasted coconut.