Jon Carroll had this as part of his Christmas Quiz.
The last time two consecutive U.S. presidents each completed two full terms was in 1809 to 1825, when the fourth and fifth presidents, James Madison and James Monroe, accomplished this. (The only other duo who've done it were the third and fourth presidents, Thomas Jefferson and James Madison, 1801 to 1817. In other words, there were actually three consecutive two-full-term presidents, 1801 to 1825.)
Another bit of trivia......the last time the Republican party won a Presidential election without a Nixon or Bush on the ticket (as President or VP) was 1928. I wonder if Jeb Bush has this on business cards to hand out at party meetings?