Preheat the oven to 350°F/180°C, grease and lightly flour 3 8-inch round cake pans and set aside
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt and set aside.
In a large bowl, cream together the butter, brown sugar, granulated sugar, and instant pudding mix until light and fluffy (3-4 minutes on medium high speed).
Add in the eggs one at a time, mixing well after each addition. Stir in the vanilla extract. Pour in half the flour mixture and mix well, followed by half the milk, then repeat until all flour and milk has been added
Divide the batter equally between the three prepared pans and bake in the oven for 30 minutes, or until a toothpick inserted in the middle comes out clean.
Allow the cakes to cool for 10 minutes in the pans before turning out and cooling completely on a wire rack