Combine first 5 ingredients in a large bowl; beat with a mixer at low speed 30 seconds or until moistened. Scrape sides of bowl with a rubber spatula; increase to medium speed, and beat 1 minute or until well blended. Pour batter evenly into 2 (8-inch) square cake pans coated with cooking spray. (Layers will be thin.)
Bake at 350° for 15 minutes or until a wooden pick inserted in center comes out clean. Cool in pans on a wire rack 5 minutes. Remove from pans; cool completely on wire rack.
Place one layer on a plate; top with 1/2 cup raspberry spread. Top with second cake layer. Cut cake in half, forming two rectangles. Spread remaining 1/4 cup raspberry spread over top of one rectangle. Place the other rectangle on top of spread to form 4 layers of cake with raspberry spread between the layers. Spread whipped topping over top and sides of cake, and sift cocoa lightly over cake. Slice cake crosswise into 8 slices.