Bake the cake according to package directions in a 9x13-inch pan. Let cool completely, then crumble into fine crumbs in a large bowl using your hands or a fork.
Add the frosting to the crumbled cake and mix with your hands until the mixture holds together when squeezed. The texture should be like cookie dough, not wet or crumbly.
Roll the mixture into 1.5-inch balls (about 2 tablespoons each) and place on a parchment-lined baking sheet. Refrigerate for at least 2 hours or freeze for 30 minutes until firm.
Melt the candy coating in a microwave-safe bowl in 30-second intervals, stirring between each, until smooth. Add vegetable oil if the coating is too thick.
Dip the tip of each lollipop stick about 1/2 inch into the melted coating, then insert halfway into a chilled cake ball. Let set for 5 minutes.
Holding the stick, dip each cake pop into the melted coating, submerging completely. Lift out and gently tap your wrist to remove excess coating, letting it drip back into the bowl.
Immediately add sprinkles or decorations while the coating is wet. Stand the pops upright in a styrofoam block or lay flat on parchment paper to set completely, about 15-20 minutes.
Once set, store in an airtight container or serve immediately. For gift packaging, wrap each pop in a small cellophane bag and tie with ribbon.
