Preheat oven to 325 degrees F. Grease and flour a 10 inch Bundt pan. Sprinkle chopped nuts evenly over the bottom of the pan, if using.
In a large bowl, combine cake mix and pudding mix. Mix in the eggs, 1/2 cup water, oil and 1/2 cup rum. Blend well. Pour batter over chopped nuts in the pan.
Bake in the preheated oven for 60 minutes, or until a toothpick inserted into the cake comes out clean.
About 5 minutes before the cake is done, make the glaze. In a saucepan, combine butter, 1/4 cup water and 1 cup sugar. Bring to a boil over medium heat and continue to boil for 5 minutes, stirring constantly. Remove from heat and stir in desired amount of rum (1/4-1/2 cup).
While cake is still hot use a skewer to poke holes all over the top of the cake (which will become the bottom). Brush on glaze allowing some of it to soak down the sides, between the cake and the pan. Let sit for 10 minutes in the pan, then turn out onto serving plate. Brush glaze over top and sides. Allow cake to absorb glaze and repeat until all glaze is used, this may take up to 10 minutes.
Allow to cool completely before serving. Tastes best on day 2, so make it a day in advance if possible.
Store any uneaten cake in an airtight container at room temperature.