The day before cake will be served, slice it into 4 horizontal layers. Mix 1/2 cup water and rum and sprinkle 1/4 cup over each layer.
In separate bowls, whisk each pudding mix with 1 cup milk. Place a cake layer on a serving platter; spread with one pudding. Repeat with two more cake layers and remaining puddings. Top with final cake layer, wrap and chill.
The next day, remove plastic wrap from cake. Frost with whipped topping and sprinkle with almonds. Garnish with maraschino cherries, if desired. Refrigerate until ready to serve.