Neutering may reduce it, but it’s moreso you need to remember that cage bars allow a rabbit to see where they can’t go. You actually can’t rule out boredom because a rabbit can have 12 “toys”, but the rabbit may not consider them as something to do. Rabbits are very task oriented. If the task is “I wanted to go out further in the room”, a “toy” will not help.

You may need to put something in the inside of the cage so he doesn’t have access to the bars, like a big piece of cardboard.

How long is he out for? More free roam time helps.

And for a rabbit that chews, it’s up to you to keep your cords in check, whether it’s winding them so the suspend in air, use wall hooks to elevate them, or cover them on corrugated loom or something else.

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First of all, while I’ve only had spayed/ neutered bunnies, from what I’ve read spaying/ neutering makes a difference in bunny temperament, so that is likely to help. 

Second, from my own experience, my first bunny was not much of a bar biter, but he was a bunny Houdini, always figuring out how to get out of his pen. It wasn’t until I expanded his living space and got him a friend (both of them spayed and neutered) that the escapism stopped. He has since passed, but his surviving mate and her new mate (also neutered) are fairly mellow, and I attribute it to the fact that they are both spayed/ neutered and they both have enough space to roam (their room is about 8 x 9 feet plus roaming time around the apartment), bunny friendship, and engaging/ rotating toys to keep them interested.
I should note that getting a bunny friend for your bunny (also known as bunny bonding) is hard work, and may end up in you having two bunnies that have to live separately from each other.

I should also add that roaming freely in the apartment (under supervision) is possible because the living room is bunny proofed, that is, all cables have been enveloped in some kind of plastic or pvc encasing that keeps them from chewing on cables. And even then, I like to keep an eye on them, and keep them away from things like radiators (they like to chew on those when the radiators are cool), and furniture (I have toys around furniture to provide diversion).
Just some ideas to keep your bun safe!

(sorry about the double post, I don’t know why my computer keeps doing that )

Unfortunately bunnies chew by nature so the only way to stop them chewing through cables and wires is to make them inaccessible. Just keep them out of your bunny’s reach

For the bar biting – a lot of buns bite their bars out of frustration. Does he get a lot of time out of his cage? He has plenty of toys but does he actually play with them?

How big is the cage/hutch? Most rabbit enclosures are far too small so that could be an issue too.