Preheat oven to 325°F. Grease and flour three 8-inch round pans. It's easiest to get the cake out of the pans if you line them with rounds of parchment paper too.
In a large bowl, whisk together the cake mix, flour, sugar, cocoa powder and salt. Add the remaining ingredients and beat with a hand mixer for 2 minutes, or until well blended.
Divide the batter evenly between the prepared pans. Be sure to fill them ¾ to 1-inch below the top of the pan. Bake 30 to 35 minutes, or until a toothpick inserted into the center comes out clean. Watch closely- check after 35 minutes and then every 5 minutes until they test done. Time will vary based on which pans you choose to use. Let the cakes cool in the pans for a few minutes, then turn out onto cooling racks to cool completely before frosting.
ADD THE FROSTING:
In a large bowl, with a hand or stand mixer, cream together the sugar and butter on low speed. Mix until well blended. Increase the speed to medium and beat for another 3 minutes. Add the vanilla and 3 tablespoons of cream and continue to beat on medium speed for 1 minute more. Add more cream if needed for desired spreading/piping consistency.
You may find that the layers are a bit moist on the surface, so just be careful when handling and frosting. Place one layer of the cake on a serving plate. Spoon a dollop of the frosting on the first layer and spread to cover. Place the second layer of cake on the first. Spread another thin layer of frosting on the second layer. Add the third layer of cake. Spread frosting on the top and then down the sides of the cake to cover.
NOTE: you may wish to do a thin crumb layer on the cake and refrigerate before frosting the whole cake (if it appears that chocolate crumbs are showing up in the frosting on the sides.)
Notes
You should have enough frosting left over to add some decorations. Scoop the remaining frosting into a piping bag and pipe decoratively onto the cake. See my White Wedding Cake recipe for similar pics: https://www.recipegirl.com/white-wedding-cake/
Refrigerate the cake until ready to serve—you’ll get cleaner cuts.