I assume you mean "cable modem", rather than "console".
Yes, you can connect the PS3 to your modem via ethernet. The modem must be powercycled though, when swapping from PC to PS3.
A router is a much better option. Then you can have your PC & PS3 connected at the same time, & not have to worry about swapping leads over, rebooting the modem, etc.
e.g.
http://www.amazon.co.uk/Linksys-WRT5...4814097&sr=1-1
With a wireless router, such as the one above, you could connect the PS3 to it using ethernet, or use the PS3's built-in wireless.