Preheat oven to 325°F and prepare a bundt pan by spraying with non-stick spray.

In a large bowl, combine cake mix, pudding mix, vegetable oil, vodka, Bailey's Irish Cream, and eggs. Mix until well combined.

Pour batter into prepared bundt pan and bake for 35-45 minutes until a toothpick inserted comes out clean.

Allow the cake to cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.

To prepare the icing, combine the butter, sugar, heavy cream, Bailey's, vanilla extract, and corn syrup in a saucepan. Heat over low until the sugar melts, then increase to medium and bring to a boil for 3 minutes, stirring occasionally.

Remove from heat, pour into a heatproof bowl, and whisk in 1 1/4 cups of powdered sugar. Allow to slightly cool and thicken.

Drizzle the glaze over the cooled cake while still warm. Let it set for a few minutes.