Synology can sync with Box.
https://www.synology.com/en-us/knowledgebase/DSM/help/CloudSync/cloudsync
Yes, that's an important distinction to make and although I was aware somewhere in the back of my mind that Synology had their own routers now, I should have made that point clear.Yes, but only Synology NAS.
Synology router does not support Cloud Sync,
it only supports Cloud Station Server, which only sync Synology NAS and the devices that connects to it.
https://www.synology.com/en-us/knowledgebase/DSM/help/CloudStation/cloudstation
https://www.synology.com/en-us/products/RT1900ac#spec
https://www.synology.com/en-us/products/RT2600ac#spec