Preheat oven to 325 degrees. Grease and flour bunt pan, and drop crushed walnuts into the bottom of the pan. Set aside.
In the base of a mixer, cream the sugar and butter for 3 minutes. Mix in the 3 tablespoons oil, flour, cocoa, baking powder, salt, and pudding mix.
In a small saucepan, combine the whole milk and chocolate chips and stir over low heat until the chocolate is melted. Set aside and let cool slightly. In a separate bowl, whisk together the remaining 1/2 cup oil, rum, vanilla, and eggs. Stir in the cooled chocolate milk mixture.
Add the wet ingredients to the dry mix and mix until smooth with no lumps. The batter should be very thin and pour easily. Pour batter into the prepared bundt pan and bake 5- to 60 minutes, or until a tester inserted in the cake comes up clean. Let cool in pan for 10 minutes, then invert onto a rack. Let cool for 20-30 minutes.
While the cake cools, prepare the rum syrup. In a large saucepan with high sides, combine the butter, water, granulated sugar, salt, and cocoa powder. Cook over medium heat until the butter completely melts and the sugar dissolves. Let reduce slightly, keeping an eye on it so it doesn’t boil over. Remove from the heat and stir in the rum (it will bubble).
Wash and dry the bundt pan, then place over the cool cake and invert the cake back into the pan. Pour the hot rum syrup all over the cake and let soak for 8 hours (overnight). In morning, invert the cake back onto a serving platter. Keeps covered for 1 week at room temperature.
Variation: This can also be made in mini bundt pans; bake at the same temp about 17-20 minutes, depending on how mini your pans are.