Preheat your oven to 350°F. Mix flour, sugar, baking powder, and salt in a bowl. In another bowl, cream together butter and eggs, then add milk and vanilla. Combine wet and dry ingredients until just mixed—don't overstir or the cake gets tough.
Pour batter into a greased 8x8 inch baking pan. Bake for 18 to 20 minutes until a toothpick comes out clean. Let it cool completely, then crumble the entire cake into a large bowl.
Add 1 1/2 cups frosting to the crumbled cake and mix with your hands until it holds together. The texture should be like wet sand that clumps when you squeeze it. If it's too dry, add more frosting one tablespoon at a time.
Roll the mixture into 12 balls about the size of walnuts. I use a cookie scoop to make them uniform, which saves so much time. Place them on a parchment-lined baking sheet and freeze for at least 15 minutes.
Divide remaining frosting into 3 small bowls and tint one red, one blue, and leave one white. Frost each cake pop with the matching color, then let them sit for 5 minutes so the frosting sets.
Heat white chocolate melts with vegetable oil in a microwave-safe bowl for 30-second intervals, stirring between each one. Once melted and smooth, dip each frosted cake pop halfway into the white chocolate. Place back on parchment and drizzle with red and blue chocolate using a fork.
Refrigerate until the chocolate coating hardens, about 10 minutes. Store in an airtight container and watch them disappear—this easy kids treat vanishes fast at any gathering.