You first make colored cake-pops (white mix + food coloring). After they're cooked then put a little batter in pan add cake pops then batter on top (not shown - but be sure batter covers them!) then bake and the cake pops will "disappear" as the cake rises (you can undercook cake-pops a tiny bit so they don't get dried out in second baking).
I also learned from playing with my daughter that sprinkles make pretty cool rainbow speckles in white cake mix. You can see them in the bowl of cake-pops. We didn't use them in the finished cake though.
On the Great American Baker competition, one of the challenges they recently had was something very similar to this -- not polka dots, but baker's choice for the kind of "surprise" upon cutting. Somebody did a dog bone, somebody else did hearts...you get the idea. I was curious too as to how they would incorporate those shapes into the batter without the shapes coming out all gobbeldygook. What they all did was basically akin to the cake pop idea : they each made a separate cake(s) colored to their taste. Once that cake was cooled they cut out their desired shapes with cookie cutters. For the main cake, they first poured a little batter into the tin, arranged the shape(s), then continued with the batter so that the batter covered the shapes.
Some of them came out really nice like the photos right here :points: A couple of people IIRC slightly underbaked their shape cakes on the idea that the shape wouldn't overbake the second time around. Those were the cakes where the shapes became smeared, and it's understandable with underbaked batter being not as loose as raw batter, but loose enough so as not to hold its shape.