60 GB+ isn't a huge amount for Infinity, especially at full speed. Depending on the speed he gets, he could easily download approximately 4 gigabytes of data in 30 minutes each day, which would equate to over 100 GB per month. I assume he is on the capped Infinity at 40 GB usage per month.
As bookbinder and Chuck say, the usage monitor would be the first port of call to determine actual usage by his laptop. Then he'll know for certain if it's another device connecting unknowingly.
He might also want to check his laptop's hard drive to see if there are any large files that have been downloaded. 60 GB+ is a lot of junk he doesn't need, especially if it's every month, and he'll run out of space if it continues like that. A friend of mine had clicked on something (trying to watch some football on a website) and had unknowingly installed a BitTorrent client that was downloading random junk all the time. Could he have done something like that? It's possible if he's not tech savvy.
You say there's usage when everything is turned off completely? Do you know that for sure? I don't know if BT can provide times when his usage appears excessive to compare with when he's actually online.
If possible, could he leave the hub switched off for a period of time, such as a week or two, to see if there's any usage? If there isn't, then there's definitely something on the laptop that needs clearing out.