Preheat oven to 350 degrees. Grease and flour 3 (9-inch) cake pans; set aside.

Prepare cake batter according to package directions, using 3 eggs, 1/2 cup butter, and amount of water specified on package. Stir in pecans. Divide batter equally among prepared cake pans. Swirl batter around rims of pans (to help layers bake more evenly) and tap pans on countertop (to remove air bubbles). Bake according to package directions. Let layers cool in pans for 10 minutes. Remove from pans and let cool completely.

To assemble cake, place 1 cake layer, smooth-side up, on a cake plate. Top with 1/4 of softened ice cream, smoothing surface with a knife or spatula. Repeat with remaining two layers of cake. (For best results, place cake in freezer for 20 to 30 minutes after adding each layer of ice cream.) After third layer of ice cream, arrange small scoops of ice cream on top around edge of cake. (Scoops should be touching). Return to freezer until serving time.

To serve, pile banana slices in center of cake, and pour 3/4 cup cooled rum sauce over bananas. (Rum sauce will run down sides of cake between ice-cream scoops.) Serve remaining rum sauce with cake as an accompaniment.