Preheat oven to 350 degrees F (175 degrees C). Line a muffin tin with paper liners.
In a large bowl, cream together the butter and sugar until light and fluffy. Beat in the eggs one at a time, then stir in the root beer extract. Combine the flour, baking soda and salt; stir into the batter.
Fill each liner with 1 tablespoon of batter. Pour 1 tablespoon of root beer into each liner. Bake for 18 to 20 minutes in the preheated oven, or until a toothpick inserted into the center of a cupcake comes out clean.