As alpacassei says - the pets at home "large" cage isn't big enough for a syrian hamster and if the cage is too small they don't have enough enrichment so will bar chew out of stress or to try and escape. The other issue is if the cage isn't big enough the wheel probably isn't either.
There are many people who have upgraded their hamsters to something like the Barney or Alexander cages (both 100cm cages with narrow 7mm bar spacing) and found that with the extra space and narrow bars, the bar chewing stops.
However - it can also become an aquired habit. So it would probably make sense to get a tank style cage, which only has bars on top on the lid. An ideal one would be the maxi duna multy - it doesn't have as much scope for enrichment as the Barney and Alexander because it is lower so not so much room for shelves and levels - but it does have a good sized floor area and you could add a freestanding platform.
The downside is it costs £80 to £90! Bin cages are also a good option - you can get a really good sized Really Useful Box for about £39 - it's 82cm by 60cm max - so a good size - not too big not too small. If you don't mind diy - it needs panels cutting out of the side and the lid with a hot knife, and then mesh attaching to the cut out panel areas.
I think if it was me I would try the Barney cage - it costs just over £50 and has plenty of floor space and narrow bars - I haven't heard of a Syrian hamster not being happy in the Barney cage. It's also good value for money as it comes with a good house for a Syrian hamster and a good shelf. You just need substrate, an 11" wheel and some tunnels/toys etc. Although a cage that size takes a lot of substrate, it can work out cheaper I find - you can buy Fitch bedding in bulk and with larger cages with more substrate you don't need to change the substrate as often - you can just spot clean and go 2 months or more without needing to change the substrate. Especially if you provide a litter tray - hamsters will use one (if you put it in the right place!) and then the cage stays clean and dry. So a large bag of substrate can last a very long time.
If you think the Barney cage is too big, the Alexander is a brilliant cage - still 100cm but the depth is a bit less (50cm as opposed to 54cm) and it comes with a great built in house, two other houses and a racetrack of shelves - again I have rarely heard of a hamster not being happy in it. But it costs more than the Barney cage at about £70.
I personally think the Barney cage would be the way to go because it's good value for money. If you think you wouldn't have space for it, the Alaska is a possibility but it doesn't have the narrow bar spacing and isn't that much of an upgrade - so to kick the bar chewing I think the Barney would be the safer bet. Also the Alaska doesn't really work out cheaper as you still need to get a house for it.
I am sure your hammy would love all the extra space and a nice big shelf to climb on and sit under.
Have linked the cages mentioned below.Zooplus sells good, reasonably priced hamster cages and wheels (also linked a good basic Syrian sized wheel - if you get it at the same time as a cage there's no postage to pay).
And your hammy will love a 28cm wheel! They run much better in a large wheel and it's more comfortable for them. Anything smaller than an 8" to 10" diameter wheel can cause them back pain and spinal problems (another reason they might bar chew as they really need their wheel for exercise).
https://www.zooplus.co.uk/shop/small.../hamster_cages
28cm Trixie wheel
https://www.zooplus.co.uk/shop/small..._wheels/174195
https://www.amazon.co.uk/Ferplast-Ma...axi+duna+multy
The only truly chew proof cage would be something like a 3 or 4 foot glass fish tank and they cost a lot of money - unless you have the space for a detolf
It's an ikea glass cabinet tipped on its side with the door left off and you need to make two lids out of wood and mesh
https://www.ikea.com/gb/en/products/...-art-10119206/
https://www.google.co.uk/search?q=Ha...w=1138&bih=503
I personally would take a chance on the Barney cage - I think his bar chewing will stop with the space and smaller gap between the bars. If you are very unlucky and it doesn't, then you haven't paid a high price for the cage and could sell it on again and maybe look at a tank style.