Place the remaining cake ingredients in the bowl of a stand mixer or a large mixing bowl. Mix on low speed to combine. Then beat for 4 minutes at medium speed.
Pour the batter into the bundt pan and bake for 1 hour, until the cake begins to pull away from the pan. Do not underbake.
Remove the cake from the oven and let cool for 10 minutes in the pan. Then invert it onto a serving plate and poke holes into the top of the cake with a long wooden skewer.
While the cake is still warm, make the glaze: Combine butter, sugar, and water in a saucepan over medium-high heat and stir until the mixture comes to a boil. Boil for 5 minutes, stirring constantly. Add the rum and return to a boil.
Spoon and brush the warm glaze evenly over the warm cake. Allow the cake to absorb the glaze and repeat until all the glaze has been used.