Preheat oven to 325°F (160°C). Spray a 12-cup Bundt pan very well with floured cooking spray, or grease and flour the pan; set aside.

To a large bowl, add the cake mix, pudding mix, eggs, water, oil, rum, and extract. Beat with a handheld electric mixer on high power until smooth and combined, about 2 minutes.

Turn the batter into the prepared Bundt pan, smoothing the top lightly with a spatula. The batter will seem thin, but the cake will rise dramatically while baking.

Bake for about 45 minutes, or until a toothpick inserted into the cake comes out clean or with a few moist crumbs. Cool cake in the pan on a wire rack.

When the cake has about 10 to 15 minutes left to bake, start making the rum glaze. Use caution, focus, and keep small children out of the kitchen as the mixture is very hot and potentially flammable.

To a medium high-sided saucepan, add the butter and heat over medium heat until melted.

Add the sugar and water to the saucepan. Bring to a rapid boil over medium-high/high heat. Allow the mixture to boil for 4 to 5 minutes, whisking constantly to prevent burning. The mixture should become white, frothy, and fluffy.

Remove the pan from the heat. Using extreme caution, slowly add the rum while whisking vigorously, as the sauce will bubble up. Return the pan to the heat for 1 minute, whisking constantly, to cook off some of the raw alcohol taste.

Add the salt and stir to combine. Transfer the sauce to a 2-cup glass measuring cup; you will have about 2 cups of sauce.

Poke holes with a fork all over the surface of the cake (which will later be the bottom when inverted). Stab the cake in about 75 places with a fork.

Slowly pour about 1 cup of the warm rum glaze over the surface, taking your time so that the sauce soaks in. Set the remaining 1 cup of sauce aside. Allow the cake to rest for about 1 hour to absorb the glaze.

Invert the cake onto a cake stand or serving platter. Stab the top and sides of the cake with a fork again in about 75 places.

Slowly and carefully pour the remaining glaze into the holes. If the glaze has crystallized, whisk it for a few seconds before adding it. You may need to press it in with a spatula. Some glaze will pool onto the cake stand, which is normal.

Allow the cake to rest for about 1 to 2 hours to fully absorb the glaze before slicing and serving. The flavors intensify over time, peaking around day three.