In a large bowl, cream together the softened butter and granulated sugar until light and fluffy.
Beat in the eggs, one at a time, until fully incorporated.
Mix in the vanilla extract.
In a separate bowl, whisk together the flour, baking powder, baking soda, and salt.
Gradually add the dry ingredients to the butter mixture, alternating with the sour cream, beginning and ending with the dry ingredients. Mix until just combined.
Gently fold in the mashed bananas.
Prepare the Banana Pudding Swirl:

In a small bowl, whisk together the instant banana pudding mix and milk until smooth and thickened.
Assemble the Cake:

Pour half of the cake batter into the prepared pan.
Drop spoonfuls of the banana pudding mixture over the batter.
Gently swirl the pudding into the batter with a knife or toothpick.
Add the remaining cake batter on top and smooth the surface.
Bake:

Bake in the preheated oven for 55-65 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for 15 minutes before transferring it to a wire rack to cool completely.
Prepare the Glaze (Optional):

In a small bowl, whisk together the powdered sugar, milk, and vanilla extract until smooth.
Drizzle the glaze over the cooled cake.
Serve:

Slice and enjoy your delicious banana pudding pound cake!