Preheat the oven to 325℉. Place cupcake liners in cupcake pans. You'll need 36.
In a large bowl, whisk together cake mix, flour, sugar and salt. Add remaining ingredients and beat with hand mixer for 2 minutes, or until well blended.
Use an ice cream scoop to fill prepared cupcake tins (it's a nice, neat way to get the batter into the pans). Fill about ¾ full. Bake about 18 minutes, or until toothpick inserted in the center comes out clean. Set them aside to cool.
PREPARE THE FROSTING:
Since this recipe includes instructions for making a LOT of frosting to frost all 36 cupcakes, it's probably best to make it in three batches. Plus, doing it this way will ensure that you can make it as you go to see how much you need (based on how much frosting you're putting on the cupcakes).
Instructions for making in three batches: In a large bowl, with a hand or stand mixer, cream together 3 cups sugar and 2 sticks butter on low speed. Mix until well blended. Increase speed to medium and beat for another 3 minutes. Add 1 teaspoon lemon extract and 1 tablespoon cream and continue to beat on medium speed for 1 minute more, adding a little more cream if needed for desired spreading/piping consistency. (Repeat for next 2 batches.)
Scoop into a piping bag and pipe decoratively onto cupcakes.