Preheat oven to 350. Line two muffin pans with 24 muffine liners.
In a large mixing bowl, whisk together the melted butter, granulated sugar, oil, eggs, and water.
In a separated bowl, whisk together the dry ingredients until thoroughly combined. Gradually mix the dry ingredients into the wet. Fold in the mashed beets and mixed well.
Pour the batter into the cupcake tins. Bake about 15-20 minutes, until set but moist. Let cupcakes cool down on a separate rack.
Beat butter for a few minutes until light and fluffy. Add 4 cups powdered sugar until the sugar has been incorporated with the butter. Add vanilla extract, and milk or heavy a little at a time until desired consistency has been reached.