Preheat your oven to 350°F (175°C). Grease and flour a 9x13 inch baking pan.
In a large mixing bowl, combine the cake mix, flour, baking powder, and salt. Mix well.
In another bowl, cream together the softened butter and powdered sugar until light and fluffy. Add the eggs, milk, and vanilla extract, and mix until smooth.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Pour the batter into the prepared baking pan and spread it evenly. Bake for 25-30 minutes, or until a toothpick inserted in the center comes out clean. Let it cool completely in the pan.
Once cooled, crumble the cake into a large bowl until it resembles fine crumbs.
Using your hands, mix in a few tablespoons of frosting until the mixture holds together when rolled into a ball.
Roll the mixture into 1-inch balls and place them on a baking sheet lined with parchment paper. Freeze for about 30 minutes to firm up.
While the cake balls are chilling, melt the white chocolate chips with the vegetable oil in a microwave-safe bowl in 30-second intervals, stirring in between until smooth.
Dip the end of each lollipop stick into the melted chocolate and insert it into the center of each cake ball. This helps to secure the stick.
Dip each cake pop into the melted chocolate, allowing any excess to drip off. Immediately sprinkle with red and blue sprinkles.
Place the finished cake pops upright in a foam block or a cup to set. Allow the chocolate to harden completely before serving.