How much is it to get iPhone 8 Plus glass back repaired?

iPhone Service Pricing - Apple Support

This page will tell you all of the prices that Apple will charge when servicing an iPhone.

For damage to the rear glass panel on an iPhone 8 Plus that requires a full unit swap of the phone.

$399 without AppleCare+

Only $99 if you do have AppleCare+ though.

Hope this helps!

Is it 400 dollars to go to Apple and get the back of my phone fixed without Apple care?

They don't fix the back, they replace the device.

Yes, if you are in USA but it may be different in other regions. See the pricing document linked above or check for the local version in your country.