It won't work I'm afraid. You can only have one device connected to the cable modem, either by USB or ethernet.
Instead, connect all your computers to the router, then connect your router to the cable modem...after all, that is what the router is designed for.
Check to see if your router has a USB port on the back to connect a PC to it. If it doesn't and you only have ethernet ports, and your PC doesn't have an ethernet NIC, then you'll either have to buy a wireless network adaptor or buy and install a PCI ethernet NIC (which is a better idea, costing less since your router is nearby).
|Desktop PC| |Macbook Air 13" (Mid 2013)|
|Windows 8.1 Pro (x64)| |AMD FX 4100 Black Edition 3.6 GHz @ 4.0 GHz OC| |Arctic Cooling Freezer 13 PRO| |Gigabyte Nvidia GeForce GTX 560 Super Overclock 1GB| |ASUS M5A78L-M/USB3 Motherboard| |Samsung 840 Pro 256GB SSD SATA III HDD| |Kingston HyperX 8GB PC3-14900 DDR3-1866| |OCZ ModXStream Pro 700W Modular PSU| |NZXT Vulcan Micro ATX Case|