Preheat oven to 300 degrees F (150 degrees C). Grease four 7x3-inch loaf pans.
Stir together 2 tablespoons white sugar and 1 teaspoon cinnamon in a small bowl. Dust pans lightly with sugar mixture.
Beat butter and 1 1/2 cups sugar with an electric mixer in a large bowl until smooth. Blend in eggs, mashed bananas, sour cream, vanilla extract, and 2 teaspoons cinnamon. Whisk together salt, baking soda, all-purpose flour, and whole wheat flour in a bowl. Stir flour mixture into butter mixture until just combined; fold in nuts. Divide into prepared pans.
Bake in preheated oven until a toothpick inserted in center comes out clean, about 1 hour.