In a large bowl, crumble your cooked and cooled cake with your hands or two forks.
In a medium bowl, beat the softened butter with a hand mixer until fluffy. Slowly beat in the powdered sugar, add in the milk and vanilla and beat for another 1 minute, it should be the consistency of peanut butter.
If frosting is too stiff, add more milk a teaspoon at a time, if it is too thin, add in more powdered sugar a teaspoon at a time.
With a hand mixer, mix in 3 tablespoons of the frosting into the crumbled cake and mix until it is a uniform mixture that is easy to roll into balls when squeezed, if it's still too crumbly add another tablespoon or two. Using a small cookie scoop or tablespoons, roll 2 tablespoons of mixture into a ball, or press with a cake pop press, and repeat with all remaining mix.
Melt 4oz of white chocolate in a small bowl in the microwave, about 45 seconds. Dip a cake pop stick into the melted chocolate and then place the stick into each one, about halfway into the cake ball. Place balls in the freezer for 1 hour or the fridge for 2 hours.
Melt 8 oz of the remaining white chocolate in a small bowl or mug in the microwave, heat in 30 second intervals at 50% power, stirring after each heating and stopping when the chocolate is just melted.
Dip cake pops into chocolate and let the excess drip off, immediately roll or sprinkle with sprinkles. Let the chocolate harden slightly, place on a sheet tray lined with parchment, or you can use a box with holes punched into it, or a piece of styrofoam to stick the pops in. Place in the fridge until ready to serve.
Notes
Once the pops are cool, you can put some of the melted chocolate in a plastic bag, cut the corner off, and drizzle onto the cake pops.
To color the chocolate: Use gel food coloring sparingly, liquid food coloring can make the chocolate seize up.
Use good quality chocolate: A good quality chocolate will not seize up when melted gently. If it does, you can add ½ teaspoon vegetable oil.
Work in batches with the chocolate, melting more as needed. Make sure you melt enough chocolate that it will submerge the entire cake pop in the chocolate when you dip it. The more you have to move the pop around, the more likely it is to come off the stick in the chocolate.
If the cake pop mixture is too dry, add more frosting. If the cake balls fall apart as you try to place them onto the sticks, they're probably too dry. If this happens with your first one, return it to the bowl and add a bit more frosting to the mixture.