Mix pudding mix and pineapple in medium bowl (do NOT make pudding according to package directions!). Stir in cool whip until well mixed.
Cut cake horizontally into 3 layers.
Place bottom cake layer, cut side up, on serving plate. Spread 1 1/3 cups of the pudding mixture onto cake; cover with middle cake layer. Spread 1 cup of pudding mixture onto imddle cake layer. Top with remaining cake layer. Spread with remaining pudding mixture.