Three problems, first, Cox doesn't offer static ip's to residential accounts. Second, running a server on a residential account is against their TOS. From Cox's Acceptable use Policy: "You may not operate, or allow others to operate, servers of any type or any other device, equipment, and/or software providing server-like functionality in connection with the Service, unless expressly authorized by Cox." Third, Cox blocks inbound port 80.
If you upgrade to a business class account, it is possible. Using DDNS is a work-a-round for a static IP. Using a port other than 80 works around the port block but anyone accessing your server would have to know the port. There is no getting around the TOS, setting up a server violates it.