Special equipment: a bundt pan
For the cake: Preheat the oven to 350 degrees F. Spray a bundt pan with cooking spray.
Bring the cola to a boil in a medium saucepan over medium-high heat and reduce down to about 1 1/4 cups, about 12 minutes. Reserve 1/4 cup in a separate bowl. Add the butter and oil to the remaining cola in the pan and cook over medium-low heat until the butter is melted. Add the granulated sugar and stir until it is mostly dissolved. Take off the heat and let cool, then whisk in the sour cream, vanilla and eggs.
Whisk together the flour, baking soda, baking powder and salt in a large bowl. Add the cola mixture and whisk until incorporated. Pour the batter into the prepared bundt pan and bake until a wooden skewer inserted into the center comes out clean, about 1 hour 10 minutes. Let the cake cool in the pan for 5 minutes.
Set a cooling rack over a parchment-lined baking pan. Invert the cake onto the rack. Poke the cake all over with a wooden skewer, then spoon the reserved cola reduction all over the cake. Let cool completely.
For the glaze: Combine the butter, cocoa powder and 2 tablespoons of the cola in a medium saucpan and cook on medium low until the butter is melted. Stir to combine, then stir in the confectioners' sugar until incorporated. Add the additional cola, about a half tablespoon at a time, until the mixture is a thick drizzling consistency.
Drizzle the glaze over the cake.