Preheat your oven to 325 degrees Fahrenheit. Grease and flour a 10-cup Bundt pan thoroughly.
In a large bowl, combine the yellow cake mix and instant vanilla pudding mix.
Add the eggs, vegetable oil, 1/2 cup Bacardi rum, and water to the dry ingredients. Beat with an electric mixer on medium speed for two minutes.
Pour the batter into the prepared Bundt pan.
Bake for 45 to 55 minutes, or until a wooden skewer inserted into the center comes out clean.
While the cake bakes, prepare the glaze. In a small saucepan, melt the butter over medium heat.
Stir in the granulated sugar and the remaining 1/2 cup of Bacardi rum. Bring the mixture to a boil, stirring constantly. Boil for exactly one minute, then remove from heat.
When the cake is finished baking, let it cool in the pan on a wire rack for 15 minutes.
Poke holes all over the top of the warm cake using a skewer or long toothpick, spacing the holes about one inch apart.
Slowly and evenly pour the hot rum glaze over the entire surface of the cake, allowing the glaze to soak into the holes.
Let the cake cool completely in the pan before inverting it onto a serving plate. Serve at room temperature.
Notes
For a stronger rum flavor, you can substitute dark rum for some or all of the Bacardi Superior Rum in the glaze.
If you prefer a cake made entirely from scratch, substitute the cake mix and pudding with 3 cups of all-purpose flour, 1 1/2 cups sugar, 1 teaspoon baking powder, and 1/2 teaspoon salt.
This cake keeps well at room temperature for up to three days if covered tightly.