Update: It seems it may now be fixed:

Xbox Live has been experiencing lots of technical issues and outages recently,the last time they were having major issues was just over a week ago when manany Xbox Live services like joining Xbox like a purching digital acsess content were not functioning correctly for many.

Now, Xbox Live is having more problems, the Xbox Live service status page indicates that there are problems with Xbox Live core services which include Signing in; creating; managing, or recovering an account and search.

The Xbox Support Twitter account tweeted about this issue:

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