Preheat your oven to 325°F. Lightly grease and flour a 12-cup Bundt or fluted tube pan.
In a large mixing bowl, beat the butter and sugar together until the mixture becomes very light and fluffy.
Mix in the rum and vanilla extracts.
Add eggs one at a time, blending well at a low speed after each addition. Continue mixing for about 3 minutes, or until the batter is smooth.
In a separate bowl, sift together the flour, baking powder, baking soda, and salt.
Begin incorporating the dry ingredients into the batter in small portions, alternating with the buttermilk. Start and end with the flour mixture, mixing just until combined.
Pour the batter evenly into the prepared pan and smooth the top.
Bake for 60 to 75 minutes, or until a toothpick inserted into the center comes out clean.
While the cake is baking, make the butter sauce. Combine the sugar, water, and butter in a saucepan and heat gently over medium-low, stirring until the butter fully melts.
Remove from heat and stir in the vanilla extract.
Once the cake is out of the oven and still hot, slowly pour the butter sauce over it while it's in the pan so it soaks in.
Let the cake absorb the sauce before turning it out of the pan. Serve warm or at room temperature.