Prepare the white cake per directions on the box. Stir in one cup of coconut flakes. Pour into 9 by 13 cake pan & bake. Combine coconut milk (shake well) with cream of coconut in bowl & set aside.
As soon as cake is out of oven, use wooden spoon to poke "holes" into cake (like a pudding poke cake). Let cake cool to room temperature (approx 30 minutes). Generously pour all of coconut milk & cream mixture over cake.
Refrigerate overnight. Top with Cool Whip right before serving.