Preheat oven to 350°F/175°C. Line a muffin pan with cupcake papers. See notes for 9x13 cake pan option.
In a small bowl stir together the egg replacer with 6 tablespoons of warm water. Set aside
In a mixing bowl add the water, vegetable oil, applesauce, sugar, and egg replacer. Mix by hand or with an electric mixer on low speed until well combined.
Add the cake mix, flour, and baking powder. Mix on medium speed for one minute.
Spoon the cake batter into prepared cupcake papers. Bake in heated oven 15 to 18 minutes, until done.
Frost cooled cupcakes with white frosting. and sprinkle with flaked coconut. Set aside.