Preheat oven to 350º F, and make sure the rack is in the center.
Line just the bottom of 3 8"-round cake pans with parchment paper.
Measure the flour, baking powder, soda and salt into a medium bowl and whisk together or sift together. Set aside.
With an electric mixer cream the butter, then add the sugar and mix on high speed until pale and fluffy, 3 - 5 minutes. Scrape down the sides of the bowl as necessary.
Add the eggs one at time, beating after each addition.
Mix in the rum or rum extract and beat until thoroughly blended.
Reduce speed to low and add ⅓ of the flour mixture then ½ of the milk, then another third of the flour, the second half of the milk and end with the flour mixture. Scraping sides of bowl as needed.
Mix until batter is just smooth, do not overmix.
Pour batter into the prepared pans and smooth the tops.
Bake for 15-20 minutes. Layers will not brown.
Cake is done when a toothpick or knife inserted into the center comes out clean.
Remove from oven, cool on rack for 7 - 10 minutes, then run a knife around the edge and turn out onto rack to finish cooling. Peel parchment paper off of cake.
Cool cake layers completely before filling and frosting.