Cable modem connections will not typically get a new public IP address just by rebooting the modem, since the downstream CMTS keeps a history of CPE IP address that have been assigned. A better solution is just to change the MAC address of your router (or PC) facing the modem. Assuming your ISP is using default/typical settings, that would get you a new public IP.
Most cable modems will have the option right in the management GUI to release and renew the public IP, which is easier than spoofing your MAC. Also, there is a lease time on all IP addresses. A good number of Cable companies will keep it low so they don't need as many IPs in their pool. Older, less efficient companies may not renew IPs upon rebooting, which is when forcing it to release and renew is helpful. However, it's pretty common that they will simply hand out a new, random IP from their pool for each request. Nonetheless, forcing it to renew is more efficient and painless than any other alternative. Or, if that isn't an option, just unplug the router from the modem, plug directly into the modem, power cycle. New IP just like magic without any spoofing necessary.