Preheat oven to 350 degrees F (175 degrees C). Grease and flour a 10 inch Bundt pan.
In a medium bowl, stir together the cake mix, 12 ounces root beer, oil and eggs until smooth. Pour batter into the prepared pan.
Bake for 35 to 40 minutes in the preheated oven, until a toothpick inserted comes out clean. Cool cake in pan for 15 minutes before inverting onto a wire rack to cool completely. Poke holes in the cake with a skewer at 2 inch intervals. Pour Root Beer Glaze evenly over cake.
To make the Root Beer Glaze: combine the confectioners sugar and 3 tablespoons of root beer in a small bowl. Beat until smooth.