Glazed Root Beer Float Bundt Cake

Name: Glazed Root Beer Float Bundt Cake
Ingredients: 2 cups root beer (Sever uses cane-sweetened Boylan); 1 cup dark unsweetened cocoa powder (Sever suggests Valrhona); 1/2 cup unsalted butter, cut into pieces; 1 1/4 cups granulated sugar; 1/2 cup firmly packed dark brown sugar; 2 cups all-purpose flour; 1 1/4 tsp. baking soda; 1 tsp. salt; 2 large eggs; 2 cups confectioners' sugar; 1/3 cup dark unsweetened cocoa powder; 1/4 tsp. salt; 1 tsp. pure vanilla extract; 1/4 cup root beer; 3 Tbsp. unsalted butter, very soft