Heat oven to 350º F. Coat three 9-inch round cake pans lightly with no-stick cooking spray.
Whisk together flour and baking powder in a medium bowl. Set aside.
Beat butter with an electric mixer on medium until light and fluffy. Gradually add sugar, continue mixing until very light, about 4 minutes.
Add eggs, one at a time, beating one minute after each addition.
Beat 1/3 of flour mixture into egg mixture on low until blended. Beat in 1/2 cup of milk until blended and repeat, ending with the addition of flour. Stir in vanilla extract.
Divide batter evenly among pans. Bake 20 to 25 minutes, or until toothpick inserted in the center comes out clean. Cool on wire rack 10 minutes before removing from pans. Cool completely.
Stir sugar and sour cream together in medium bowl until blended, while cake is baking. Reserve 1/3 cup coconut and set aside. Add remaining coconut to sour cream mixture. Blend well. Fold 1 cup sour cream mixture into whipped cream for frosting. Chill sour cream mixture and frosting until cake layers are cool.
SPREAD sour cream mixture between layers of cake leaving 1/4-inch at edge uncovered. Spread frosting on top and sides of cake. Frosting may run down sides of cake, but will thicken as cake chills. Sprinkle reserved coconut over top of cake.
Chill at least one hour uncovered. Serve or cover and chill up to three days to allow the flavors to blend.