In a large mixing bowl, beat together butter, sugar, and eggs. Add in root beer, flour, baking powder and salt. Beat until well combined.
Pour into a greased 8 x 8 square baking dish. Bake at 375 for 32 - 35 minutes or until a knife inserted in the center comes out clean. Cool completely.
For the frosting, beat together butter, salt, sugar, and root beer. Add milk gradually until you have a slightly thin buttercream. Pour/spread over cooled cake and allow frosting to set. Slice and serve.