I thought Don Henley wrote that song. His version is on one of his greatest hits compilations.
https://en.wikipedia.org/wiki/Everybody_Knows_(Leonard_Cohen_song)
from link: (Don Henley mentioned)
Like many of Cohen’s songs, “Everybody Knows” has been covered by several artists
Concrete Blonde, in the film Pump Up the Volume (1990), the TV series Dirty Sexy Money at the end of the third episode of the first season, and on their compilation album Still in Hollywood (1994)
As “Alle vet jo det”, by Kari Bremnes, on Cohen på norsk (Cohen in Norwegian, 1993)
Don Henley, on Actual Miles: Henley’s Greatest Hits (1995) and the tribute album Tower of Song (1995), and as a duet with Bryan Adams at Live at Honor 1996.
Washington Squares, on From Greenwich Village: The Complete Washington Squares (1997)
Dayna Kurtz, on her album Beautiful Yesterday (2004)