Preheat oven to 325°F (165°C). Thoroughly grease and flour a Bundt pan. If using nuts, sprinkle them evenly over the bottom of the pan.
In a large bowl, combine cake mix, pudding mix, eggs, oil, water, and 1/2 cup rum. Beat on medium speed for 2 minutes until smooth and well combined. Pour batter into the prepared Bundt pan.
Bake for 50-60 minutes, or until a toothpick inserted into the center comes out clean. Allow cake to cool in the pan for 10 minutes.
While cake is cooling, prepare the rum soaking syrup: In a saucepan over medium heat, combine butter, sugar, and water. Bring to a boil and continue boiling for 5 minutes, stirring constantly. Remove from heat and carefully stir in 3/4 cup rum.
Use a skewer or toothpick to poke holes all over the bottom of the cake (still in the pan). Slowly pour about 1/3 of the hot rum syrup over the cake, allowing it to absorb.
After 5 minutes, place a serving plate over the Bundt pan and carefully invert the cake. Poke holes all over the top and sides of the cake.
Gradually spoon the remaining rum syrup over the entire cake, pausing between additions to let the syrup absorb.
Allow the cake to cool completely, then cover loosely with plastic wrap and let rest for at least 8 hours or overnight before serving.