I've not heard of anyone else having problems sending mail on Cox. You must be doing something wrong like trying to forward from someone else's server through Cox rather than sending it directly. Eveyone I know of blocks forwarding through their servers to keep spam down. If you use Gmail, which is better anyway, it should work without any problems. Email me directly and I'll help you with it if you want.
You must not read the Cox forum here, there are many posts on the topic including a bunch of mine and responses from the Cox technical people that visit the forums.
You are also incorrect about my doing something wrong. What exactly is wrong from sending an e-mail from my primary Cox e-mail address to a second address on the same account or to my mom's Cox account across town?
Gmail's is fine for some things but I prefer not to subject all of my outgoing mail to their scanners. If you don't mind that scanning and the headers they add to your outgoing mail then yes, Gmail SMTP servers work.
How exactly do you propose to help me when the Cox techs here in the forums and the ones that answer their support e-mail and phone lines have been unable to resolve the problem even after escalating it several levels? Do you even use Cox for sending mail, I don't see it on the list of reviews in your profile.
No I don't use Cox and don't read the forums since we can't get Cox out here but all my friends use it in Phoenix without problems. Since I've been a network admin. for the college district for 10 years and I've had some experience with email. That sounds like an interesting problem and I just thought I'd offer to help. How are you using Cox email anyway, do you go on their website or are you sending it from Outlook or what? Also, I didn't see anything on the Cox forum about anyone having email problems except a few from 2009, can you point me to it?