Heat oven to 350° F. Butter an 8 or 9-inch round cake pan and line with a circle of parchment.
In a small bowl, whisk together the flours, baking powder and salt.
In a large bowl and using an electric mixer on medium speed, cream the butter, scraping down the sides of the bowl as necessary, until the butter is lighter in color, about 45 seconds. Then add the maple sugar in a steady stream and scrape down the bowl again. Continue to mix on medium speed until the mixture is very light in color and texture, about 4 to 5 minutes.
In a small bowl whisk the eggs. Slowly pour in the eggs a little at a time, and beat very well for about 2 minutes.
Combine the vanilla and milk in a small bowl or measuring cup.
With the mixer on low, add the flour mixture in two doses, alternating with the milk. Scrape down the sides of the bowl in between additions.
Pour the batter into prepared pans, smoothing the tops. Place cake in the oven and bake for 35-45 minutes, or until a toothpick inserted in the center comes out clean. Check after 35 minutes; you want the cake to lightly spring back in the center when pressed.
Remove cake from the oven and set on a rack to cool for 10 minutes. Run a butter knife around the side of the pan to loosen the cake, then turn out onto the rack to finish cooling completely.