The Google .net client library works with Windows phone.
PM> Install-Package Google.Apis.Calendar.v3
I don't know of any Google Calendar and windows phone samples but there is a console application sample project
I cant post links but you can find it on gitHub Google-Dotnet-Samples
My website has a couple of tutorials to go along with it Google Calendar API C# again I cant post links just try and Google for Google Calendar api and C# should find them.
good luck