For the Cake:
For the Rum Glaze:
Pre heat the oven to 325 F. Thoroughly grease and flour a Bundt pan and set aside.
In a large mixing bowl, combine cake mix, pudding mix, eggs, water, oil, and 1/2 cup dark rum. Mix by hand or an electric mixer until the batter is smooth.
Pour the batter into the prepared Bundt pan.
Bake for 1 hour. Remove the cake from the oven and allow it to cool for 20 minutes. Invert the cake onto a wire rack and let it cool completely.
Transfer the cooled cake to a serving platter. Using a fork or toothpick, prick the top of the cake to form small holes that will absorb the rum glaze.
Make the Glaze
In a heavy saucepan, melt the butter.
Whisk in the water and sugar.
Slowly bring the sugar and butter mixture to a light boil and cook for 5 minutes, constantly stirring.
Remove the sugar mixture from the heat and stir in the rum.
Allow the glaze to cool slightly before glazing the cake.
Drizzle and smooth some of the glaze over the top and sides of the cake. Allow the cake to absorb the glaze and then repeat until the glaze is gone. Serve the rum cake as is or with a scoop of vanilla ice cream or a dollop of freshly whipped heavy cream.