Preheat the oven to 350 degrees.
Sift the flour and sugar together into a bowl. In a pot, heat 2 sticks of the butter, 2 tablespoons of the cocoa powder, and 1 cup of the Coca-Cola to the boiling point. Pour over the flour-sugar mixture. Add the buttermilk, baking soda, eggs, vanilla, and marshmallows (the batter will be thin and the marshmallows will float to the top). Grease a 9-by-13-inch pan with butter and lightly flour the surface. Pour the batter into the pan and bake for 30-35 minutes.
Just before the cake is done, combine the remaining butter, cocoa powder, Coca-Cola, and the confectioners’ sugar in a pot and bring to a boil. Remove the cake from the oven, and pour the icing over the top while hot. Serve.