Preheat the oven to 350 degrees F. Place 12 cupcake liners into a cupcake pan.
In a medium bowl, cream the white sugar and butter. Beat in the eggs, one at a time, then stir in the vanilla. Combine the flour, pudding mix and baking powder. Then add to the creamed mixture and mix well. Pour in the buttermilk and stir until the batter is smooth. Stir in the mashed banana. Pour or spoon the batter into the cupcake liners in the cupcake pan. Bake until the cake springs back to the touch, 18 to 20 minutes. Test cake doneness approximately 15 minutes into baking time. Cool.