Preheat oven to 350°F (175°C). Grease and flour a 9x13-inch baking pan.
In a large bowl, whisk together flour, sugar, baking soda, and salt.
In a saucepan, combine 1/2 cup butter, oil, 3 tablespoons cocoa, and 1 cup cola. Bring to a boil, stirring constantly. Remove from heat and pour over flour mixture; stir until well combined.
Beat in buttermilk, eggs, and 1 teaspoon vanilla until smooth. Pour batter into prepared pan.
Bake for 30-35 minutes, or until a toothpick inserted in center comes out clean. Cool completely in pan on a wire rack.
For frosting: In a saucepan, melt 1/2 cup butter. Stir in 3 tablespoons cocoa and 6 tablespoons cola. Bring to a boil, then remove from heat. Gradually beat in powdered sugar and 1 teaspoon vanilla until smooth. Spread over cooled cake.
Tips
Use a full-sugar cola like Coca-Cola for best flavor; diet cola may alter texture.
Store covered at room temperature for up to 3 days.