Another person here with EXACTLY the same issue. Originally used the router in "modem" mode, and get this HP email to check your ISP isn't blocking these ports, so as an experiment connected printer directly to hub, using a cable. Set the router to "router" mode, and connected a laptop to another Ethernet port. Set the IP address the printer was given by the Superhub 3.0 to the DMZ, restarted printer.. And guess what EXACTLY the same issue.. Printer refuses to connect to my HP instant ink account. It gets a valid HP eprint ink email address, but can't use my HP instant ink account.
What's frustrating is that I can't get any technical support at Virgin Media to confirm that at this point the Virgin Media router or the Virgin media interconnect kit (switches routers) are NOT blocking ANY of those ports.
Once I've got written email confirmation this is the case, I can ping the problem back to HP as in "next idea" .. HP