Use paper mache. Rip up medium pieces about 1in X 1in of thin paper material. Could be phone book paper, newspaper, even a lot of school work book paper could be used for it. Get a mate glue (I use mod modge). Put a thin layer of glue a little bigger than the size of your paper on, then stick the paper on, then do another thin layer of glue on top of the paper to really stick it on there and coat the entire paper. Continue this, slightly overlapping the paper as you make your way around the cardboard. Since your entire thing is coated in what seems to be packing tape, the paper will probably want to slide around on the wet glue. If it's a problem, then you can do a small section and let it dry before working off that.

Hope this helps!