Take your children to infinity and beyond! Or just offer them a piece of this rocket cake.
Preheat oven to 350 degrees. Butter a 9-by-13-inch baking pan. Line bottom with parchment or waxed paper; butter lining. Dust with flour; tap out excess. Set aside.
Sift together flour, baking powder, and salt into a medium bowl; set aside. Stir together milk and vanilla in a small bowl; set aside. Put butter in the bowl of an electric mixer fitted with the paddle attachment; beat on medium speed until creamy, about 2 minutes. Add sugar in a slow, steady stream; mix until pale and fluffy, scraping down sides of bowl as needed, about 3 minutes.
Reduce speed to low; add flour mixture in 3 batches, alternating with the milk mixture and beginning and ending with the flour (do not overmix). Set aside.
Beat egg whites in the clean bowl of an electric mixer fitted with the whisk attachment until stiff peaks form. Fold one-third of whites into batter. Fold in remaining whites in 2 batches.
Pour batter into prepared pan, and smooth with an offset spatula. Bake until cake is springy to the touch and a cake tester inserted into center comes out clean, 35 to 40 minutes. Let cake cool in pan on a wire rack 15 minutes. Run a knife around sides of cake to loosen; invert onto wire rack. Reinvert cake; let cool completely, right-side up, before decorating. (Cooled cake can be frozen, wrapped in plastic wrap, up to 2 days.)
With a serrated knife, trim top of cake to make it flat. Halve cake horizontally to make 2 layers. Spread 1 cup buttercream over bottom layer; place second layer back on top. Cut cake into components using template. Arrange on a platter or foil-covered board to form rocket shape. If desired, cut board slightly larger than assembled cake shape before wrapping in foil.
Spread 1 1/4 cups buttercream in a thin layer over entire cake; refrigerate until firm, about 20 minutes. Meanwhile, prepare buttercream for decorating. Assemble 5 pastry bags with couplers. Tint 3/4 cup buttercream each red and blue, and 1/2 cup gray; transfer each to a pastry bag. Fill another bag with 1/4 cup each red, orange, and yellow buttercream; fit with an Ateco #233 multi-hole tip. Fill last bag with 1/2 cup plain buttercream.
Frost cake with a smooth layer of buttercream. Fit gray bag with an Ateco #4 plain tip; outline rocket. Add designs: a filled-in nose, a round window, or the outline of a flag. Sprinkle rocket nose, bottom, and window with sanding sugar.
Fit red, white, and blue bags with Ateco #18 star tips; pipe stripes. Use an Ateco #16 star tip for flag. Pipe a white star border around bottom edge of cake. For letters, use an Ateco #8 plain tip. Pipe "flames" out of bottom of rocket using bag of multicolored buttercream. If desired, attach figurine with licorice. Chill until ready to serve, up to 4 hours.
Because this recipe requires only egg whites, you may want to use pasteurized egg whites to avoid having yolks left over. Look for them at grocery stores next to whole eggs.