Root Beer Bundt Cake

Name: Root Beer Bundt Cake
Ingredients: 2 cup root beer (do not use diet root beer); 1 cup dark unsweetened cocoa powder; 1/2 cup (1 stick) unsalted butter, cut into 1-inch pieces; 1 1/4 cup granulated sugar; 1/2 cup firmly packed dark brown sugar; 2 cup all-purpose flour; 1 1/4 tsp baking soda; 1 tsp salt; 2 large eggs; 2 oz dark chocolate (60% cacao), melted and cooled slightly; 1/2 cup (1 stick) unsalted butter, softened; 1/4 cup root beer; 2/3 cup dark unsweetened cocoa powder; 2 1/2 cup confectioners; Vanilla Ice Cream, to serve