To fix Windows Update error 0x8007003B, run the Windows Update troubleshooter under Settings, reset update components by stopping the Windows Update…
Sometimes a later cumulative update supersedes the one that's failing.
A corrupted update cache is one of the most common causes.
If corrupted system files are the cause, SFC repairs them.
Outdated drivers are one of the listed causes, and they're easy to overlook because the error mentions nothing about hardware.
Read the complete breakdown, fixes and what happens next.