General fact: 6736 is a number for which we're missing a fact (submit one to numbersapi at google mail!).
Mathematical fact: 6736 is the number of 3×3 sliding puzzle positions that require exactly 17 moves to solve starting with the hole in the center.
Trivia: 6736 is an unremarkable number.
Historical date: June 10th is the day in 1977 that James Earl Ray escapes from Brushy Mountain State Prison in Petros, Tennessee, but is recaptured on June 13.