Preheat oven to 325 degrees F (165 degrees C). Grease and flour two 8x4 inch loaf pans. Sift together the flour, baking powder and baking soda, set aside.
In a medium bowl, cream together the butter, white sugar, confectioners sugar and brown sugar until smooth. Add egg whites and egg yolks, beating after each addition. Stir in the vanilla. Stir in the dry ingredients alternately with the milk. Divide the batter evenly between the two pans.
Bake for 60 to 70 minutes in the preheated oven, until a toothpick inserted in the center of the cake comes out clean. Cool in the pan for 10 minutes before inverting onto a wire rack to cool completely.