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Does Google Public DNS offer the ability to block or filter out unwanted sites?

No. Google Public DNS is purely a DNS resolution and caching server; it does not perform any blocking or filtering of any kind, except that it may not resolve certain domains in extraordinary cases if we believe this is necessary to protect Google’s users from security threats. But we believe that blocking functionality is usually best performed by the client. If you are interested in enabling such functionality, you should consider installing a client-side application or browser add-on for this purpose.