Cockburn shared on Instagram a racist social media post directed at him after the top-seeded Illini lost to No. 8 Loyola Chicago on Sunday.
Cockburn, who was born in Jamaica but later moved to New York, posted a screenshot of the post and responded by writing: "I blame his parents.''
An Illinois spokesman told ESPN's Adam Rittenberg that the school is looking into the situation and has spoken with Cockburn. The spokesman said the source of the comment was identified by others on social media.
Cockburn's post came a day after Ohio State's E.J. Liddell received threatening and insulting social media messages following the second-seeded Buckeyes' loss to No. 15 seed Oral Roberts. He posted images of the messages, including one that said, "I hope you die I really do." Other messages included racist insults.
"Honestly, what did I do to deserve this?'' Liddell posted on Twitter. "I'm human.''
Ohio State has contacted police about the language directed at Liddell.
The Associated Press contributed to this report.