Fatto generale: 6736 is a number for which we're missing a fact (submit one to numbersapi at google mail!).
Fatto matematico: 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.
Data storica: June 10th is the day in 1980 that the African National Congress in South Africa publishes a call to fight from their imprisoned leader Nelson Mandela.