Preheat oven to 350 degrees F (175 degrees C). Spray a 9-cup fluted tube pan with cooking spray that contains flour, and brush the spray into the grooves of the pan with a pastry brush. Spray 1 more light coating of cooking spray, and invert the pan to let any excess spray drip out.
In a mixing bowl, beat together the orange cake mix, lemon pudding mix, eggs, vegetable oil, margarita mix, lime juice, tequila, and triple sec until thoroughly combined. Fold in the grated zest of 1 lime, and pour the batter into the prepared fluted tube pan. Use a spatula to fill grooves of the pan with batter, and tap the filled cake pan to remove air pockets.
Bake in the preheated oven until a toothpick inserted into the center of the cake comes out clean, about 45 minutes.
Cool the cake in the pan on a rack for 10 minutes, shake it a couple of times to help the sides release, and slide a thin silicone or nylon spatula between the cake and the pan.
Place a serving plate over the top of the cake pan and invert the pan to slide the cake onto the serving plate. Allow the cake to finish cooling.
Make a thin glaze by mixing together confectioners' sugar, 1 tablespoon of tequila, 2 tablespoons of triple sec, juice of 2 limes, and grated zest of 1 lime.
Drizzle the glaze decoratively over the cake, let the glaze set for a few minutes to harden, and slice.
