How much does it cost to repair broken back cover of iPhone 8?

Apple generally only does this as a complete service replacement (aka "other repair"). The price in the United States (if direct from Apple) is $349 plus tax. The first price is the AppleCare+ deductible while the other is for out of warranty/AppleCare+

iPhone Repair - Official Apple Support

iPhone 8 $ 99 $ 349

It depends on your country, and also if you have AppleCare+ for your phone or not.

For the US: https://support.apple.com/iphone/repair/service

99$ with AppleCare+, and 349$ without AppleCare+.

Note that Apple will replace your device instead of repairing it.