The Modem has a MAC address that it presents to the cable service provider and the provider typically uses that MAC address to 'authenticate' the modem and then presents it with an IP address ...
I just got a Zyxel Modem from Century Link and 5 usable Static IPs in a block of 8. I configured the modem for "transparent bridging" and configured the PPOE credentials on a DD-WRT router and now it ...
Most people understand that when you connect to the internet, your internet service provider assigns your modem and network an internet protocol (IP) address. That's your external or public-facing IP.