Check router manual regarding the devices allowed for that port. It may be limited in the load it can support on its own.
Your external drive needs two USB ports: one for data, one for power.
A simple hub may not work. A USB hub with a supplemental power supply might work.
The USB cabling would be something like one USB cable from router to hub input port. Then the external HDD would use two of the USB ports. The hub then powered via the supplemental power supply.