For a coconut cake with coconut milk, combine a box of coconut cake mix with 1 1/3 cups coconut milk, 1/4 cup water and three egg whites. Beat in 1/2 cup flaked coconut, pour the mixture into a pan, and bake it according to package directions. Cool it before frosting.
Preheat your oven to 325 degrees Fahrenheit. Pour a box of coconut cake mix into a large mixing bowl. Add the coconut milk, water and egg whites, and beat the batter until it is smooth. Mix in the flaked coconut.
Spray the bottom of a cake pan with baking spray, but do not spray the sides. Pour the batter into the pan, and bake it as directed by the mix manufacturer. Cool the cake for at least an hour.
Prepare the frosting while the cake cools. Pour 1 cup white chocolate chips into a microwave-safe bowl, and heat the chips for 30 seconds. Stir the chips, and microwave them again if they are not fully melted. Add 1 3/4 cup confectioner's sugar, 1/3 cup softened butter, 1/3 cup coconut milk and 1/2 teaspoon pure vanilla extract. Stir until the frosting is smooth and creamy. Frost the cake once it cools to room temperature. Decorate the frosted cake with the remaining coconut flakes.