Can a webhook be triggered by a formula field?

Yes, if you're using a service like Workato that will monitor for changes in your table's records, a change in the value of a formula field can trigger additional actions in the recipe.

If it is possible with the native QuickBase then, it would be great otherwise last option is to use the 3rd party solution?

Thanks,
Gaurav

Natively this will not run because the formula value is not actually calculated (or Evaluated) unless something else changes.  

You will need to have something outside run an API, save the value, and then another API to see if the value has changed.  Hence, a 3rd party.

You could potentially do this with a synced table, and trigger the webhook via the change there.  This is untested, and could get really nasty very quickly.

Maybe look at a different angle to accomplish the goal.  
Just ideas.