Preheat oven to 350°F. Line one 8" round cake pan with foil and spray with nonstick cooking spray. Line two more with parchment paper (bottom only) and spray well with nonstick cooking spray or grease and flour the pans. (If you do not have 3 round cake pans, make the brownies first, let them cool, then make the cake layers.)
Make the brownie mix according to package directions. Pour into prepared cake pan (the one with foil) and bake for about 40-50 minutes until a toothpick comes out clean 2” from the edge. Cool, then remove from the pan.
Mix the cake mix with milk, oil, and eggs until smooth and no lumps remain. Stir in sprinkles. Pour equally into two remaining pans and bake according to package directions, or until a toothpick comes out clean. Cool completely before removing from pans.
Make the frosting by beating the cream cheese and butter until smooth, then slowly mixing in the powdered sugar. Mix in vanilla and beat until smooth, then stir in sprinkles.
Divide the frosting into three parts. Place the brownie layer on the bottom of a cake plate. Top with 1/3 of the frosting. Add one cake layer and another 1/3 of the frosting. Top with remaining cake layer.
Frost the top of the cake with some of the remaining frosting and give the sides a light coating with the remaining frosting. This is also called a “crumb coat”. You’ll still see the cake through the sides but that doesn’t matter because you’re coating it with sprinkles.
To coat the sides with sprinkles, take handfuls and press them onto the sides of the cake. This is a messy step! Chill the cake until ready to finish it.
Make the chocolate drizzle: place chocolate chips, butter, corn syrup, and water in a small pan. Heat over medium low heat, stirring constantly, until melted and smooth. Remove from the hot pan and let cool at least 10 minutes, stirring a few times.
Finish the cake by coating the top with the chocolate and drizzling it down the sides. Top with more sprinkles. Chill to set.