Cox blocks outbound port 25 which is total BS. Comcast used to do this but there was a way to go in your account settings and turn it off. No such luck on Cox. Some of us run legitimate mail servers (not spam relays) for various purposes like home automation and its been a real pain in the you-know-what since they implemented this policy.
I now use a smart host to receive inbound mail and relay it home over an alternate port. Outbound mail goes out through the same smarthost on an alternate port.
If you're just relaying outbound on a personal mail account you can use the alternate SMTP ports (I think, 975) to send outbound provided your mail server has them open. I didn't have good luck using Cox's relay to go outbound (started thresholding camera events) and no, I don't need a commercial account, this has worked fine on every consumer ISP I've used since the 90's (no reason it shouldn't).