QUICK ANSWER: Please ask your host why the error happens when trying to reach the www.googleapis.com domain.
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DETAILED ANSWER: If you get this error:
YouTube API request failed: Failed to connect to 2607:f8b0:4004:80e::200a: Network is unreachable
... don't worry.
This is likely an IPv6 issue on your host.
The YouTube API domain resolves to IPv6 address (2607:f8b0:400d:c03::5f:) but the host fails to map a route to it.
Chances are IPv6 support isn't properly configured on the host. For some reason it doesn't use IPv4 address of the API server, which is also available.
(IPv6 is an upgrade to traditional IP protocol using 6-byte addresses to allow much more devices directly connected to the Internet. The protocol however is not yet 100% supported by all the networking software and hardware.)
This should be resolved by your host.
Please ask them why the error happens when trying to reach the www.googleapis.com domain.
Article ID: 185
Category: 1-Click Video Site Builder