Step 1

For the cake: Preheat the oven to 325 degrees F. Grease and flour a 10- to 12-cup Bundt pan. Set the oven rack in the middle position in the oven.

Step 2

Whisk together the flour, baking powder, baking soda and salt in a medium bowl. Beat the butter and shortening with the granulated sugar in a heavy-duty stand mixer fitted with the paddle attachment until light and fluffy. Add the eggs, one at a time, beating just until the yellow disappears after each addition. Beat in the vanilla and rum extracts.

Step 3

Mix in the flour mixture alternately with the buttermilk in 3 additions, beginning and ending with the flour mixture. Spread the batter evenly into the prepared Bundt pan. Bang the pan on the countertop to remove any air bubbles.

Step 4

Bake until a wooden pick inserted in the center comes out with moist crumbs, about 1 hour and 10 minutes. Remove the cake from the oven and poke holes in the cake, being careful not to poke the holes all the way through.

Step 5

For the butter syrup: Melt the butter in a small saucepan over medium-low heat. Add the sugar and 3 tablespoons water and stir until the sugar dissolves. Continue to cook, stirring frequently, until the sauce is foamy and becomes syrupy, about 10 minutes. Stir in the vanilla and rum extracts. Reserve a quarter of the syrup for brushing on the outsides of the cake.

Step 6

Pour the remaining syrup over the warm cake into the poked holes. Let stand until the syrup is absorbed and no longer sticky, 5 to 10 minutes. Run a knife around the edges of the warm cake and turn the cake out onto to a rack to cool. Brush the reserved syrup over the outsides of the cake. Let stand until cooled, about 1 hour.