Preheat oven to 350°F. Butter the bottom and sides of two 8 or 9-inch, round cake pans. Dust with flour to coat, then invert and tap out any excess. (If making cupcakes, use liners instead of greasing and coating the tins.)
Place all of the dry cake mix ingredients in a large bowl and whisk together well to combine.
Stir in the yogurt, butter, water, vanilla, and eggs until moistened and no lumps remain (Be careful not to overmix).
Stir ½ cup rainbow sprinkles into the batter.
Divide the batter between the prepared pans.
Bake until the layers are domed and golden brown, and a few moist crumbs cling to a skewer inserted in the center of the cake, 35 to 40 minutes (40 to 50 minutes for a Bundt, 25 to 30 minutes for a 13 by 9-inch cake, and 20 to 25 minutes for cupcakes).
While the cake is baking, prepare the syrup.
Combine the sugar, water, and salt in a small saucepan, bring to a boil over medium-high heat, and boil for about 5 minutes.
Stir to dissolve the sugar, then stir in the vanilla and remove from the heat. Pour syrup over the cake when it’s warm or let it stand, covered, until it reaches room temperature.
After removing the cake layers from the oven, pierce them (still in the pans) at 1-inch intervals with a skewer or paring knife.
Pour or brush the syrup over the layers, dividing it evenly.
Set the layers aside, in the pans, on a wire rack to cool completely. (The syrup will soak into the cakes.)
When the cakes are cool and no longer wet to the touch, 1 to 2 hours, make the frosting: Combine the butter, salt and 2 cups of the sugar in a large bowl and beat with an electric mixer on low speed until incorporated, about 1 minute.
Add the remaining sugar and beat on medium speed until the frosting is pale and no longer grainy, about 2 minutes. Add the vanilla and beat until the frosting is very light and fluffy, about 2 minutes.
Run a knife, or an offset spatula, around the edge of one of the cake layers to loosen it. (Turn the layers out of their pans 1 by 1, as you frost them.)
Place the layer on a cake plate with strips of waxed, or parchment, paper underneath; these will catch any drips and keep your cake plate clean.
Spread the layer with about a third of the frosting on top.
Frost the rest.
Run a knife, or an offset spatula, around the edge of the remaining cake layer.
Invert it onto the frosted layer.
Frost the sides and top of the cake with the remaining frosting.