Place rack in the center of the oven and preheat oven to 350 .
Lightly mist three 9-inch round cake pans with vegetable oil cooking spray, then dust them with flour. Shake out the excess flour. Set the pans aside.
Mix the cake mix, peanut butter, oil, eggs, and vanilla, 1 1/3 cups of water, then beat with an electric mixer on low speed until blended, 30 seconds. Scrape down the side of the bowl. Increase the mixer speed to medium and beat for 2 minutes longer, scraping down the side again if necessary. The batter should be well blended. Divide the batter evenly among the prepared pans.
Bake the cakes until they spring back when lightly pressed with a finger, 18 - 20 min. Remove the cakes from the oven, and place them on wire racks to cool for 10 min. Remove cakes from pans. Allow the cakes to cool completely, 15 min. longer, right side up.
Meanwhile, place 28 of the peanut butter cups in the freezer for 15 - 20 min so that they will be easier to chop, then finely chop them and set aside with the whole peanut butter cups.
Make the frosting: Place the butter and peanut butter in a large mixing bowl and beat with an electric mixer on low speed until creamy, 30 seconds. Add 2 cups of the confectioners'' sugar, 1/4 cup of the milk, and the vanilla and beat on low until the mixture is combined, 30 sec. Add 1 1/2 cups of the remaining confectioners'' sugar and the remaining 1/4 cup milk and beat the frosting until it is smooth and spreadable, 30 sec. Then, increase the mixer speed to high and beat. adding the remaining 1/2 cup sugar a little at a time until the frosting is thickened and fluffy, 1 min. longer.
To assemble the cake, place one cake layer, right side up, on a serving plate and spread some of the frosting over the top. Press half of the chopped peanut butter cups into this frosing, distributing them evenly. Place a second cake layer, right side up, on top of the first. Spread some of the frosting over the top. Press the remaining chopped peanut butter cups into this frosting. Place the third cake layer, right side up on top of the second layer, then frost the top smoothly and generously. Frost the sides. Use the remaining peanut butter cups to decorate.