About 15 minutes before the cake finishes baking, prepare the glaze. In a medium saucepan, combine the sugar, butter, water, and rum. Stir continuously over low heat until the butter melts and everything is well mixed. Increase to medium heat, stirring as it comes to a gentle boil (watch it closely, as it can easily boil over if left unattended). Let the mixture boil for exactly 3 minutes, then remove from heat.
Once the cake has finished baking, leave it in the pan and immediately pour the warm glaze evenly over it, allowing it to soak in. Let the cake sit for 15 minutes so the glaze fully absorbs.
To serve, place a cake plate or stand over the pan, then invert the pan and plate together, allowing the cake to release onto the plate. Remove the bundt pan, revealing a deliciously moist rum cake, ready to slice and enjoy!