We are getting 200mbps down from our ISP, and I've confirmed that when I hook directly into the modem via Ethernet, that I will get that 200mbps. It's when I plug my modem into my router (because I can't be plugged directly into the modem all the time, lest my family has no internet connection) that I am only getting 60mbps down on the same Ethernet cable. I've checked my router specs (Linksys ea6400) and it assures me that the Ethernet ports are all 1gbps.
Edit:
I have a CAT6 cable going from my modem to my router, and another CAT6 cable going from my router to my PC, so it's not the Ethernet cables