Using an electric mixer, cream the butter and vanilla. In a separate heatproof bowl, whisk together the sugar and egg whites. Place over a pan of barely simmering water, whisking, just until the sugar dissolves. Remove from the heat and beat with clean mixer blades on high speed until the mixture cools to room temperature and forms stiff peaks, about 5 minutes.
Lower the speed and add the creamed butter a few tablespoons at a time (the mixture will look broken and curdled). Slowly mix in the rest of the butter until combined. Beat on high until smooth, about 10 minutes. Add a drop of red food coloring and beat until uniform in color. Cover with plastic wrap until ready to use.
Using a long serrated knife, slice each cake horizontally into 2 even layers. Dab a bit of the preserves onto each cardboard round and place one corresponding cake layer on top. Spread the remaining preserves on the 2 bottom layers, then spread about 1/2 cup frosting over the preserves. Top with the remaining 2 cake layers. Apply a thin layer of frosting to each double-layer cake to seal in the crumbs. Refrigerate for 30 minutes to set slightly.
Cover the tops and sides of each cake with the remaining frosting, then place the small cake and its cardboard on top of the large cake. Top with cotton candy and decorate with the candies.