Preheat oven to 350° F. Prepare three 7-inch cake pans with nonstick cooking spray and parchment circles.
In a large mixing bowl, combine brown sugar, granulated sugar, vegetable oil, eggs, vanilla extract, sour cream, and mashed banana. Whisk until smooth.
Add in baking powder, salt, and all-purpose flour. Gently whisk until the dry ingredients are fully incorporated into the wet ingredients and the cake batter is smooth.
Portion cake batter into prepared cake pans and spread into an even layer.
Bake for approximately 30 minutes until the cakes bounce back when gently touched or an inserted toothpick comes out clean.
Remove the cake pans from the oven and allow the cake layers to cool in the pan for approximately 10-15 minutes. Remove the cake layers from the pan and transfer to a wire rack to cool completely.