What modem are you using? How are you connected? What Internet plan are you on? How are you testing your speed? I checked Cox's web site, If you are on the Essential plan, your speeds should be up to 100 mbps down, and up to 5 mbps up. Not sure where you are getting 8.35, other than Cox routinely sets their speeds a bit higher to ensure you meet the speeds they advertise, IE 5 upload, MAY be provisioned as 6.35 or higher, to ensure you reach the 5 they are advertising, BUT they aren't going to guarantee higher speeds than they are advertising. 

Here's a post from 7 months ago with the same scenario.  It's kinda long with 50 replies but its gist is the "Buckle up for More Speed" promo:

• If you subscribed to the Preferred plan and had an eligible modem, Cox would increase your download from 150 Mbps to 250 Mbps
• Cox notified subscribers via a pop-up on the Cox App and an email from residential@service.cox.com
• The pop-up included a link
• No mention if email included a link

Moderators had confirmed the promo for the Preferred plan and its notifications were legit; however, a moderator confirmed there is currently no promo for the Essential plan.

In this long post from 7 months ago, curtb researched the legitimacy of the email notification.  Although the email was legit, we'd need to know the content of the email.

For example, did the email to Curt include a link to log into his account or to "view in browser"...or did the email just instruct Curt to log into his account and reset his modem?

If a moderator had confirmed there is currently no promotion for the Essential plan, someone could have just maliciously copied-and-pasted the content of the "Buckle up for More Speed" promo and included a risky link.

forums.cox.com/.../50-faster-speeds-free

Hi Perplexed, as I mentioned previously, the email you received is valid. I truly understand why it perplexed you, as it certainly had me confused for a while, also. I believe I've figured it out. Cox increased the upload speeds of the Essential tier in June 2022 from 3 Mbps to 5 Mbps. The 3 to 5 increase is basically 67%. I will double-check with our Marketing team on Monday and let you know if I find out something different. Again, I apologize for the confusion this email caused. -Becky, Cox Support Forums Moderator