Preheat oven to 325 degrees F (165 degrees C). Coat two 9-inch round cake pans with non-stick cooking spray and dust with flour
Mix cake mix and pudding mix in a large bowl. Add water, sour cream, and egg whites; beat on medium speed with electric mixer for 2 minutes. Pour about half the batter into each of the prepared cake pans.
Bake in the preheated oven until golden and the tops spring back when lightly pressed, about 25 minutes; set aside to cook to room temperature.
Mix 1 tablespoon reserved juice from raspberries and cornstarch in a small bowl; set aside.
Bring the berries to a simmer in a saucepan over medium heat; cook and stir until the berries break down, about 10 minutes. Stir the cornstarch mixture into the berries; continue cooking until thickened, about 2 minutes more. Remove saucepan from heat and cool berry mixture to room temperature.
When the cakes are completely cool, run a paring knife between cake and pan edges. Hold a cake pan on its side and gently tap the sides of the pan against the counter to loosen cake layer. Cover the cake pan with a plate and invert it to tip the cake out of the pan and onto the plate.
Place one cake layer onto a serving plate. Spread raspberry filling over the top of the layer. Top with remaining cake.
Prepare frosting by gently folding yogurt into the whipped topping in a large bowl; spread over top and sides of cake.
Cool cake in refrigerator for 2 hours before serving.