Preheat the oven to 350 degrees. Prepare a 9×13 baking dish with nonstick cooking spray.
In a large saucepan, combine the Dr. Pepper, oil, butter, and cocoa powder. Place over medium heat, mixing well, and bring to a simmer. Remove from the heat.
In a large bowl, prepare the dry ingredients by whisking together the sugar, flour, and baking soda.
Stir the dry ingredients into the Dr. Pepper mixture in the saucepan, mixing well.
In a separate small bowl, use a fork or whisk to mix the eggs and buttermilk. Stir the buttermilk mixture into the batter in the saucepan.
Transfer the batter into the prepared pan. Bake for 23 to 28 minutes or until a toothpick inserted into the center comes out clean. Place on a wire rack to rest.
To prepare the icing: In a medium saucepan over medium-low heat, heat the butter together with the cocoa powder, whisking often, for about 1 minute or until the butter melts and the mixture is smooth. Reduce the heat to low and add the cola and milk, whisking until blended. Stir in the powdered sugar to the saucepan, whisking constantly until blended. Add the vanilla and stir until blended. Pour the icing over the cake.
Cool the cake completely prior to serving.