John Stuart , 3rd Earl of Bute , KG , PC ( 25 May 1713-10 March 1792 ) was a Scottish nobleman . He was Prime Minister of Great Britain ( 1762 â `` 1763 ) under King George III . John Stuart , 3rd Earl of Bute KG , PC ( 25 May 1713 â `` 10 March 1792 ) , styled Lord Mount Stuart before 1723 , was a Scottish nobleman who served as Prime Minister of Great Britain ( 1762 â `` 1763 ) under George III , and was arguably the last important favorite in British politics .