1. Preheat oven to 345 degrees F. Butter a 10- to 12-cup Bundt pan, glass or non-stick. Dust it with flour, and turn to coat the pan evenly and well. Set aside.
2. In a medium bowl, mix flour, pudding mix, baking powder and salt.
3. In the bowl of a standing mixer, cream together sugar and butter until creamy and fluffy. Add 3 tablespoons of your oil from the 1/2 cup.
4. Start mixer at low speed and add dry ingredients slowly. Increase mixer speed to medium and mix until the mixture has fine, crumb-like consistency.
5. In another bowl, whisk together eggs, vanilla, remaining oil and milk. Just before adding to dry ingredients, add rum.
6. At medium speed, add wet ingredients to dry ingredients in mixer bowl. Gradually increase speed to high and continue mixing for 10 seconds, until the batter is smooth. Scrape the edges of bowl with a spatula to make sure there are no dry traces left.
7. Pour batter into the prepared Bundt pan and spread level with a spatula. Bake for 50 to 55 minutes.
8. While the cake is baking make the syrup: In a medium-sized saucepan combine all syrup ingredients except ¼ cup of the rum and vanilla. Bring to a rapid boil, then reduce heat to medium-low and simmer for 4 minutes, until the syrup has thickened slightly. Remove from heat and stir in vanilla and last of the rum. For a less alcoholic taste, add all the rum at the beginning.
9. Remove the cake from the oven. When done, it will test clean on a cake tester or a long wooden skewer. (Don’t use a toothpick, though; it doesn’t get down deep enough into the cake.)
10. Leave the cake in the pan to cool slightly, about 15 minutes. Once cooled, shake it gently to make sure the cake is not stuck. Flip the cake out on a rack to cool further. Wash the cake pan and make sure to dry it well. Place the pan over the cake and turn it gently back into the pan.
11. With a long wooden skewer poke several holes into the cake.
12. Pour the syrup over the cake, still in its pan, and allow it to soak in.
13. Cover the pan loosely with plastic wrap and allow the cake to sit out overnight to cool completely and absorb the syrup.
14. When ready to serve, loosen the edges of the cake and invert it onto a serving plate.
Serve with berries and whipped cream. What a decadent luscious cake!
