PREHEAT oven to 350ºF. Prepare cake batter and bake as directed on package for two 9-inch round baking pans. Cool in pans on wire racks 10 min. Loosen cakes from sides of pans. Invert onto racks; gently remove pans. Cool completely.
POUR milk into large bowl. Add dry pudding mix. Beat with wire whisk 2 min. (Mixture will be thick.) Gently stir in whipped topping.
PLACE one cake layer on serving plate; spread with jam. Top with layers of half each of the pudding mixture and strawberries; cover with remaining cake layer. Top with remaining pudding mixture. Refrigerate at least 1 hour. Top with remaining strawberries and sprinkle with sugar just before serving. Store leftovers in refrigerator.