I am making a graduation cake and I am thinking it is looking a little boring, so I wanted to add a multi loop side bow. The sizes of the teirs are 10, 6, 4 because that's what my friend wanted.

I wanted to know how to attach the bow to the side of the cake. The cake is butter cream with fondant decorations. I was thinking of using melted chocolate and a fondant ball, that would be hidden by the loops. Any suggestions are welcome, needed, and appreciated.

If you make your bow out of gum paste ( I use Wilton's pre-made gum paste) you can get the thickness of the bow loops pretty thin and they dry a lot lighter than fondant which helps when trying to adhere decor to the sides. I use buttercream but any of the things you mentioned would work.

I would also insert a skewer into the fondant ball at an angle facing down so there's no chance of the bow falling off. Hope that makes sense?

You can have ribbons on the side of a cake tier but they are actually inserted into the top of the tier below it. Clear as mud?
When you stack your cake you will have a two inch wide margin of cake going around the middle tier. That margin is the top portion of the bottom 10 inch tier that is exposed. Insert a straw into the 10 inch layer about an inch or so out from the middle tier. You can insert a small wired group of 3 or 4 loops into the straw and then add additional loops one at a time that have been made with a toothpick instead of wire. That way they can go directly into the cake around the original cluster to make it just the right size.

Sorry, hard to describe what I see in my mind's eye. Hope this makes sense.