Bake your vanilla cake mix according to package directions in a 9x13 pan. Let it cool completely—this takes about an hour but you can't skip it. Once cool, crumble the entire cake into a large bowl until it looks like coarse breadcrumbs.
Add 1/2 cup melted butter, 1 cup powdered sugar, and 1/4 tsp salt to your crumbled cake. Mix everything together with your hands until it forms a dough-like consistency (it should hold together when you squeeze it). I always taste a tiny bit here to make sure the sweetness works for you.
Roll the mixture into 24 balls about the size of walnuts and place them on a parchment-lined baking sheet. Pop them in the freezer for at least 30 minutes until they're firm—don't skip this step or they'll fall apart during dipping. Meanwhile, melt your white chocolate coating in a microwave-safe bowl in 30-second bursts, stirring between each one.
Divide your melted white chocolate into 3 separate bowls. Leave one plain white, and add red gel coloring to the second bowl and blue to the third. Stir each until the color is completely even (I always get a little bit of gel on my fingers and it stains like crazy, so wear gloves).
Insert lollipop sticks into your frozen cake balls and dip each one into the white chocolate first. Let the excess drip off for about 5 seconds before placing back on parchment. Now dip into your red or blue coating and add sprinkles immediately—they stick better when the chocolate is still wet.
Chill the finished patriotic cake pops cozy in the fridge for 15 minutes to set completely before moving them. Store them in an airtight container with parchment between layers so they don't stick together. These'll stay fresh for 3-4 days if you can resist eating them faster (mine never make it past day two).