Heat oven to 350°F (325°F for dark or nonstick pans). Generously spray bottoms and sides of two 9-inch round cake pans with baking spray with flour.
In large bowl, beat cake ingredients with electric mixer on low speed until moistened, then on medium speed 2 minutes, scraping bowl occasionally. Pour into pans.
Bake and cool as directed on box for 9-inch rounds.
On serving plate, place 1 cake, rounded side down. Spread with half of the frosting; top with half of the mangoes and half of the coconut. Top with second cake, rounded side up. Spread with remaining frosting; top with remaining mangoes and coconut. Store loosely covered in refrigerator.