Preheat oven to 350.
Put cupcake liners in a muffin tin.
Combine the two cups of flour, two cups of sugar, 2 tsp of cinnamon, and 2 tsp of baking soda in a bowl and mix well.
In a large bowl, beat the four eggs and slowly add in one cup of oil while continuing to beat.
Add flour mixture to egg mixture and mix well.
Fold in the 4 cups of shredded carrots.
Fill cupcake liners about 2/3 full.
Bake for 20 minutes or until the toothpick inserted in the center comes out clean. Cool cupcakes in pan for 10 minutes, then move to a cooling rack to finish cooling.
Beat 1 cup of softened butter and 16 oz of softened cream cheese in a large bowl until light and fluffy.
Add eight cups of powdered sugar and 1 tbsp of milk and beat on high until smooth.
Ice cupcakes with icing.