Microsoft has released the titles they will make available for premium Xbox Live Gold Members. The titles are listed below.
Xbox 360
Just Cause 2 is available from June 1st-June 15th.
Thief is available from June 16th-June 30th.
If you are an Xbox One user you will find a familiar option.
Xbox One
Pool Nation FX is available all month. This is its third consecutive month.
Massive Chalice is available all month.