My Iphone software cannot update due to unknown error (4000).

See this Apple article: If you see an error when you update or restore your iPhone, iPad, or iPod

If you see an error when you update or restore your iPhone, iPad, or iPod - Apple Support (SG)

Guess you use a Windows PC, if so check als the AV & Firewall on the PC. 

Disable your AV & Firewalls temporarily while you restore & update your apple device.

If they are On, turn Off Hotspot & VPN. 

Check also -> iPhone 7 Repair Program for "No Service" Issues

iPhone 7 Repair Program for "No Service" Issues - Apple Support

I had this problem. My iPhone8 failed an update to 14.5.1. I got the message Cellular Update Failed. My cellular service was cut off at that point.

I found the solution here. IOS UPDATE VIA ITUNES "ERROR 4000" SOLVED - Apple Community

I just turned off the passcode. After I successfully used iTunes to update my phone, I turned the passcode back on. I had to reenter payment cards, but I got my iPhone back. Everything else came back.

I had a backup of my phone but didn't need it, but your mileage may vary.