Beat butter with an electric mixer on medium speed until creamy, about 2 minutes. Sift together powdered sugar, cocoa, and salt in a bowl.

Stir together vanilla and 5 tablespoons of the cola in a small bowl. Add powdered sugar mixture to butter alternately with vanilla mixture, beginning and ending with powdered sugar mixture, beating on low speed until just blended after each addition.

Beat in remaining 1 tablespoon cola to mixture, 1 teaspoon at a time, if needed, until desired consistency is reached.