Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking dish.
Beat cake mix, water, eggs, and oil in a bowl using an electric mixer on low speed for 30 seconds. Increase speed to medium and beat for 2 minutes more. Pour batter into the prepared baking dish.
Bake in the preheated oven until a toothpick inserted in the center comes out clean, 28 to 33 minutes. Cool completely, at least 1 hour.
Crumble cake into a large bowl. Stir frosting into cake crumbles until mixture is sticky but not too smooth. Chill in refrigerator, at least 30 minutes.
Roll cake mixture into 1 1/2-inch balls and arrange on a baking sheet. Place 1 lollipop stick into each ball.
Melt about 1/4 cup chocolate candy melts in a microwave-safe bowl in the microwave, about 20 seconds. Dip each cake pop in the melted chocolate. Repeat melting chocolate and dipping remaining cake pops. Decorate pops with decorating icing.