YouTube Data API v3 has not been used in project code example

Example: YouTube Data API v3 has not been used in project before or it is disabled. Enable it by visiting then retry. If you enabled this API recently, wait a few minutes for the action to propagate to our systems and retry.

Apparently youtube has restricted your project from using the present API key
try regenerating new API key or create a new project and generate new key.
or 
Your current api needs to be enabled first. Please check that also