Very generously grease (I use shortening) a 10-inch or 12-cup bundt pan. Flour it, shaking off excess.
Sprinkle 1 cup pecans, chopped, on the bottom of the pan and set aside.
In a large bowl, mix 15.25 ounce box of yellow cake mix, ¼ cup all-purpose flour, 2 tablespoons sugar, 3 ¾ ounce package instant vanilla pudding mix, 4 eggs, ½ cup cold water, ½ cup vegetable oil, and ½ cup Bacardi dark rum and beat until well incorporated with an electric mixer.
Pour the cake batter over the nuts.
Bake in the preheated oven for about 1 hour or until a cake tester or toothpick comes out clean, or with a few moist crumbs. The top should feel set, not jiggly. It's an estimated time; it might take more or less, depending on your oven and the type of pan you use.
Allow the cake to cool in the pan for 15 minutes on a wire rack, then carefully invert onto a serving plate to cool for another 15 minutes while you prepare the glaze.
Make the rum soak or glaze:
Melt ¼ cup butter in a small saucepan over medium heat.
Stir in ¼ cup water and 1 cup granulated sugar. Boil the mixture for 5 minutes, stirring constantly. Remove from the heat and stir in ½ cup Bacardi dark rum.
Prick the top of the cake with a skewer or cake tester many, many times. Try not to disrupt the pecans.
Drizzle and smooth the glaze evenly over the top and sides of the cake. Allow the cake to absorb the glaze and repeat until the glaze is used up.
Notes
Bundt pan size matters.The batter should never fill more than ⅔ to ¾ of the pan's capacity. This recipe is designed for a 10-inch (12-cup) bundt pan. A 9-cup pan will overflow. If all you have is the smaller pan, fill as explained above and bake some muffins on the side with the remaining batter.Make sure to very generously grease and flour the bundt pan, especially around the creases. Letting the cake cool for the first 15 minutes also helps it release cleanly. I like to use shortening more than butter; it works better with my pans. From-scratch version is absolutely doable. If you'd rather skip the box mix, use a standard yellow cake base: 2 cups all-purpose flour, 1 teaspoon baking powder, ½ teaspoon baking soda, ½ teaspoon salt, ¾ cup softened butter, 1 ½ cups sugar, 3 eggs and 1 cup sour cream. Replace the pudding mix with 2 tablespoons of cornstarch (it mimics the same binding effect). The rum in the batter stays the same. The result is a slightly more tender crumb and a less sweet finish, which some people actually prefer.Rum cake actually gets better after a day! It stays moist for 3–4 days covered at room temperature. You can also refrigerate it for up to a week, tightly wrapped.Most of the alcohol cooks off in the glaze, leaving mainly flavor. For a stronger rum taste, brush a little extra rum on the cake before glazing.