To Make Rum Cake: 

Preheat oven to 325 degrees F.  Liberally spray a 10-12 cup Bundt pan with nonstick baking spray (like Bakers Joy); or grease and flour it.  Set aside.

Using a hand-held or standing mixer, combine flour, sugar, pudding mix, baking powder, salt, butter and oil until well-incorporated and sandy looking.  With mixer on low, gradually add milk and eggs.  Increase mixer to medium high and beat until smooth, scraping down sides and bottom of bowl.  Stir in rum, vanilla, Key lime juice, and zest.  Pour batter into prepared pan and smooth top.  Bake for 45 to 55 minutes or until toothpick inserted near center comes out clean.  Remove from oven and let cool on a wire rack for about 5 minutes.   

Poke cake all over with a long skewer like a chopstick.  Gradually pour quarter-amounts of Rum Soak over cake.  Allow liquid to soak in before adding more.  Cover the Bundt pan with plastic wrap and allow to sit overnight at room temperature or in the fridge.

When ready to serve, turn cake out onto serving plate.  If cake doesn’t turn out immediately, place pan into a warm oven (about 200-250 degrees F) for about 5-10 minutes to loose the rum soak.  Pour glaze over cake and serve.  Leftover cake can be covered with plastic wrap and kept at room temperature for up to 3 days, or stored in the refrigerator for up to 5 days. 

To Make Rum Soak:

While cake bakes, in a saucepan over medium heat, combine all ingredients except vanilla and lime juice.  Bring to a boil, stirring constantly, then reduce heat to low.  Allow rum syrup to simmer and thicken slightly, about 10-15 minutes.  Remove from heat and stir in vanilla and Key lime juice.  Pour over baked, poked and slightly cooled cake. 

To Make Key Lime Glaze: 

In a medium-sized bowl, whisk all ingredients together until smooth. Glaze should be slightly thick (like the consistency of cold heavy cream).  Pour over rum cake.