Preheat the oven to 350?F (175?C). Grease a 9x9 inch baking dish.

In a mixing bowl, whisk together flour and baking powder.

In another bowl, cream together the sugar and butter until light and fluffy.

Add eggs one at a time, mixing well after each addition. Stir in vanilla.

Gradually add the flour mixture to the creamed mixture alternately with milk, starting and ending with flour.

Pour the batter into the prepared baking dish and bake for 20 minutes or until a toothpick comes out clean.

Let the cake cool completely in the pan.

In a bowl, combine sweetened condensed milk, evaporated milk, and whole milk.

Once the cake is cool, poke holes all over the surface with a fork.

Pour the milk mixture evenly over the cake and let it soak for at least 30 minutes.

In a mixing bowl, whisk the banana pudding mix with cold milk until thickened.

Fold in sliced bananas gently.

Spread the banana pudding mixture over the soaked cake.

Top with whipped cream and additional banana slices if desired.

Refrigerate for at least 2 hours before serving.