Preheat your oven to 350°F (175°C) with the rack in the center position. Generously grease and flour a 10-cup bundt pan, coating every crevice, or use a baking spray that contains flour.
In a large mixing bowl, whisk together the yellow cake mix and instant vanilla pudding mix until evenly distributed.
Add the eggs one at a time, then pour in the vegetable oil, orange juice, vodka, and Galliano liqueur. Mix on low speed until just combined, scraping down the bowl as needed.
Increase mixer speed to medium and beat for 2 full minutes until the batter is smooth, thick, and slightly lighter in color. Scrape down the sides halfway through.
Pour the batter into the prepared bundt pan, then tap the pan firmly on the counter 3–4 times to release air bubbles. Smooth the top with a spatula.
Bake for 45–50 minutes without opening the oven for the first 40 minutes. The cake is done when a toothpick inserted in the thickest part comes out clean and the edges pull away from the pan.
Cool in the pan on a wire rack for exactly 20 minutes, then run a thin knife around the edges, invert onto a serving plate, and allow to cool for another 30 minutes before glazing.
Sift the powdered sugar into a medium bowl, then whisk in the orange juice, Galliano, and vodka until completely smooth. The glaze should be thin enough to drizzle but thick enough to coat a spoon.
Poke holes about 1 inch (2.5cm) deep all over the top of the warm cake, then slowly drizzle all of the glaze over the surface in two layers, letting it soak in between applications.
Allow the glazed cake to sit at room temperature for at least 1 hour before slicing so the glaze sets and the flavors meld together.