Bake the cake: Prepare the cake mix with the eggs, oil, and water as directed on the box, then bake in a 9x13-inch pan until a toothpick comes out clean, about 25 minutes.
Cool completely: Let the cake cool completely in the pan, about 1 hour, so it crumbles evenly instead of forming wet clumps.
Crumble the cake: Crumble the cooled cake into fine, even crumbs in a large mixing bowl using your hands or a fork.
Mix in frosting: Add the vanilla frosting a few tablespoons at a time, mixing until the mixture holds together when pressed but is not greasy or wet.
Roll into balls: Scoop and roll the mixture into 24 balls, each about 1.5 inches wide, placing them on a parchment-lined tray as you go.
Chill until firm: Refrigerate the cake balls for at least 1 hour, or freeze for 15 minutes, until they feel firm and cold to the touch.
Melt the candy coating: Melt the candy melts in the microwave in 20-second bursts, stirring between each, then stir in 1-2 tablespoons of oil until smooth and pourable.
Anchor the sticks: Dip the tip of each lollipop stick into the melted coating, then insert it halfway into a chilled cake ball to anchor it.
Dip the pops: Dip each cake ball fully into the melted candy coating, turning gently to coat evenly, then tap off the excess over the bowl.
Add sprinkles: Immediately add sprinkles or decorations while the coating is still wet, about 30 seconds after dipping, then stand the pops upright to set.
Let the coating set: Place the finished pops in a foam block or stand upright until the candy coating hardens completely, about 15 minutes at room temperature.