Cole has been taken to task over ???an abusive or offensive??? message he sent on social media following the 2-2 draw between Tottenham and West Ham on February 22.
The FA commission will now decide on an appropriate punishment for the 31-year-old.
Following his charge by the FA earlier this week, Cole has decided against appealing ahead of Friday’s 6pm deadline.
Cole, who was also fined ??20,000 by the FA in 2011 for an identical offence, has made 17 appearances for the Hammers in all competitions this season, scoring three goals.