© Ray Tang / Global Look PressProtesters take to the streets of Dalston burning bed mattresses and clash with police following the death of Rashan Charles whilst being arrested by police.
Okundaye, who is head of the university's Black and Minority Ethnic Campaign, reportedly posted the tweets on Friday following clashes between police and protesters during a protest about the death of 20-year-old Rashan Charles in police custody in Hackney on July 22.
Although Okundaye has since made his account private, the Times reported that he made a series of angry tweets. These included a claim that "ALL white people are racist. White middle class, white working class, white men, white women, white gays, white children they can ALL geddit."
He also tweeted: "Watching these middle-class white people despair over black people protesting in their colonised Dalston is absolutely delicious."
Okundaye is reading politics and sociology at the prestigious institution's Pembroke College. He was born in South London and was a scholar at the £36,400 (US$47,700)-a-year Whitgift School before starting at Cambridge.
"We are aware of these matters and they are in hand. I can confirm that police are investigating the incident," Cambridge Police told the Times on Monday.
Harrow East Conservative MP Bob Blackman told the Times that Okundaye ought to be "prosecuted for inciting racial hatred."
"That is stirring up racial hatred unnecessarily and completely without justification," Blackman said.
Okundaye has previously campaigned for a statue of a bronze cockerel (rooster) displayed in the dining room of Jesus College, Cambridge, to be removed.
The statue is one of the Benin Bronzes, a series of artefacts stolen from what is now Nigeria when the British military laid waste to the Kingdom of Benin in 1897.
The cockerel was eventually taken down and the university is in talks with heritage specialists and Nigerian museum authorities to have it returned.
Comment: Black man's death during arrest prompts violent protest in London's Hackney