Preheat oven to 350°F (175°C). Grease and flour a 9x13 inch baking pan.
In a large bowl, cream together the butter and sugar until light and fluffy. Beat in eggs one at a time.
Combine the flour, baking powder, baking soda, and salt. Gradually add to the creamed mixture, alternating with the buttermilk, and mix until just combined.
Pour batter into the prepared pan and bake for 30-35 minutes, or until a wooden skewer inserted into the center comes out clean.
Let the cake cool completely in the pan.
Once the cake is cool, poke holes all over the top using a fork or wooden skewer.
Pour the banana pudding over the top of the cake, letting it soak into the holes.
Top with Nilla Wafers and refrigerate for at least 2 hours before serving.