I have pre installed windows 10 home and some weeks ago i got 2021-09 cumulative update but its not installing and showing error 0x800f081f

Informative Microsoft Article.

Microsoft article on update issues

First try DISM and SFC repairs

(1) Open cmd.exe with Run as Administrator.

(2) DISM.exe /Online /Cleanup-image /StartComponentCleanup

(3) DISM.exe /Online /Cleanup-Image /Restorehealth

(4) SFC /SCANNOW

(5) Restart

Now cleanup Windows Update.

Again open cmd.exe with Run as Administrator and run the following commands.

Net Stop bits

Net Stop wuauserv

Net Stop appidsvc

Net Stop cryptsvc

Ren %systemroot%SoftwareDistribution SoftwareDistribution.bak

Ren %systemroot%system32catroot2 catroot2.bak

Net Start bits

Net Start wuauserv

Net Start appidsvc

Net Start cryptsvc

Restart and test.

If the above fails to resolve update issues, then run Windows 10 Repair Install.

Go to the Media Creation Link:

https://www.microsoft.com/en-us/software-download/windows10

Windows 10 is running, so click on the Download button (not Upgrade Button) and select Run.

Use the first option: Keep Everything and try that.

Windows 10 Repair Install has more aggressive options if you need them.