Preheat your oven to 350°F (175°C) and grease a 9x13 inch baking pan.
In a large mixing bowl, combine the vanilla cake mix, eggs, vegetable oil, and water. Mix until well combined and smooth.
Pour the batter into the prepared baking pan and bake for 25-30 minutes, or until a toothpick inserted in the center comes out clean.
Once baked, let the cake cool completely in the pan on a wire rack.
After the cake has cooled, crumble it into a large bowl until fine crumbs form.
Add the vanilla frosting to the cake crumbs and mix until fully combined.
Divide the mixture into three equal portions. Leave one portion plain, color one portion with red food coloring, and color the last portion with blue food coloring. Mix well until colors are evenly distributed.
Using your hands, roll each portion into small balls, about 1 inch in diameter, and place them on a baking sheet lined with parchment paper.
Once all the cake balls are formed, place the baking sheet in the freezer for about 30 minutes to firm up.
While the cake balls are freezing, melt the white candy melts according to package instructions until smooth.
Dip the tip of each lollipop stick into the melted candy, then insert it halfway into a cake ball. This will help the stick stay in place.
Once all the sticks are inserted, dip each cake pop into the melted white candy, allowing any excess to drip off.
Immediately sprinkle the cake pops with red, white, and blue sprinkles before the coating sets.
Place the completed cake pops upright in a styrofoam block or a mug to allow the coating to harden completely.
Once set, your Red White Blue Cake Pops are ready to be served!