Start with a wooden frame covered with the chicken wire on one side. Block the hidden side with cardboard. I would suggest rolling newspaper around a dowel or broomstick handle to make the cells to fit inside the chicken wire. Maybe a toilet tissue roll might work ? The newspaper should make good cells and if dipped into paper mache that should give them some body ..
Anyway that would be how I would attempt to make this.
Edit - Oops, my mind was processing a Honey Comb due to the song. I will go back to my paper mache mess.
Why not use a large balloon from party city instead??? A balloon has the beehive shape already and it is easy to remove once the paper mache dries. I would do several layers of paper mache on a balloon and then use paper clay to build up the higher areas of the hive. Or instead of building up with paper clay you could use rolled up news paper to and duct tape them to the balloon after the fir
Or are you talking giant beehive kids can walk through?
Anyhow, for the former, keep in mind the shape of a wild beehive. I would almost suggest maybe using burlap soaked in glue to make the plates/wrinkles instead of mache. properly painted, the texture of the burlap would help with the illusion as well.
If you're more looking into something BIG/walkthough type, an easy way to "make" the cells is to get the LARGE bubble wrap, and fill in the spaces around the bubbles with paper mache, then color up the bubbles fo indicate filled cells, or pop them for open ones.
either way, get a good recording, the buzzing sound can be unnerving alone.