Fatto matematico: 8580 is the number of subsets of the 28^{th} roots of unity that add to 1.
Trivia: 8580 is a number for which we're missing a fact (submit one to numbersapi at google mail!).
Data storica: June 28th is the day in 1978 that the United States Supreme Court, in Regents of the University of California v. Bakke bars quota systems in college admissions.