It's the ruffle cake technique.
Edited to add: lol I didn't scroll down. I assumed you were talking about the first cake that pop up! Sorry Please disregard my comment
I don't know how they did it, but this is how I would take a stab at it. I would get my white chocolate melted and add the different colors or different colored candy melts melted and drizzle over the tops and sides of the cake. I would personally do one color at a time till I got through all of my colors and then stack them after the candy was set, but not hard. Of course I know that some of it is going to be harder because you did them first. The bottom layers you would not have to do all the way across the tops because the other cakes are going to cover most of the top. I have never had any success with those Candy writing tubes, but you can also put them in the disposable bags and cut a hole in the tip and have a little more control over the shape of the designs on the sides especially. Will look forward to seeing what the others say. that is a neat cake. Love the bright colors and ribbons.