Preheat the oven to 350°F. Grease three 9-inch round cake pans with butter, oil or cooking spray. To make the cake: Follow the directions on the cake mix box, substituting milk for water. Divide the batter among cake pans. Bake for 20 minutes. Remove from the oven and let cool in the pans for 5 minutes on a wire rack, then remove the cakes from the pans to cool completely.
In a medium bowl, stir together sour cream, sugar and coconut. Spread between the slightly warm cake layers, piercing each layer with a toothpick as you stack them, but don’t pierce the top of the top layer. Store the cake in a container in the refrigerator 2-3 days to allow the flavors to soak through.