Can not find serial number for HomePod. Nothing on bottom of pod and have discarded the box.

See also https://support.apple.com/en-us/HT208347

for the location of the serial number on the base.

I am puzzled why you need the serial number to add it to the Home app. For me this happened automatically when I used my iPhone to set up the Homepod.

If it’s been set up you can find it in the Home App

Go to Home App, long press on HomePod to bring up settings , click the gear icon, scroll down

It can also be found in your iCloud account and also on your device in settings under iCloud - in the list of devices you set up with iCloud

You answered me.You don’t need it to add to home app or set up.

I didn’t ask why the OP needs the serial number.