Use an electric mixer on low speed to combine the first six ingredients in a large mixing bowl until the mix is the consistency of fine gravel, and all the particles are almost equal in size. (basic cake mix may be stored in a container in the refrigerator for 3 months).
Preheat oven to 325º Spray a large bundt pan with non-stick cooking spray. Sprinkle the chopped nuts into the bottom.
Place basic cake mix, pudding mix milk, eggs, rum, oil and vanilla in a large bowl and combine on medium speed with an electric mixer for about 2 or 3 min. scrape down the bowl half why through. Batter should be very smooth. Pour into prepared bundt pan and level out top.
Bake until fully golden and taster comes out clean and cake springs back (about 55 min.) remove from oven and place on cooling rack while making soaking glaze.
RUM SOAKING GLAZE:
In a small saucepan, combine butter, water and sugar, bring to a boil carefully as mixture boils over very easily. Reduce to a simmer and cook until sugar is dissolved and syrup is combined well and a little thicker. Remove from heat and add rum and mix to combine.
While cake is still cooling, pour hot syrup into and on top of cake. there is a lot of syrup and if cake doesn't soak it up right away, just wait a couple of min. and add the rest. it will take time to soak it up.
Cool cake completely in bundt pan before turning onto serving platter. This cake is delicate, so once it is turned out, it cannot be moved around easily. Can be eaten when fully cool, but better the next day.