1. Remove top oven rack; move other rack to lowest position.
2. Sift cocoa over dry cake mix in large bowl; stir to blend. Proceed with mixing cake as directed on package. Bake and cool as directed for 10-inch tube pan. Carefully run knife along side of pan to loosen cake; remove from pan. Using serrated knife, cut cake into sixteen slices.
3. Prepare whipped topping mixes as directed on package, using 1 cup milk and 1 teaspoon vanilla. Fold in strawberry puree.
4. For each serving, cut one cake slice into cubes and layer with about 1/3 cup strawberry mixture in individual dessert dish.** Garnish with strawberries, if desired. Refrigerate until ready to serve. Cover; refrigerate leftover dessert. 16 servings.
*Mash 2 cups sliced fresh strawberries (or frozen berries, thawed) in blender or food processor. Cover; blend until smooth. Puree should measure 1 cup.
**Entire cake can be cut into cubes and layered with strawberry mixture in trifle bowl.