After ten years at Tottenham, the former midfielder enjoyed a journeyman career at various clubs, including Brentford and Reading.
But that's not why an American film production company decided to make a film with him in it.
When Cockram hung up his boots in 2000, he launched a brief career as a fireman in west London and dabbled in the business world.
Interesting. But also not the reason why he was on the big screen at the Tribeca Film Festival in New York, which was founded by actor Robert De Niro.
The 59-year-old's greatest accomplishment is the Brentford Penguins: a football team for people with Down's Syndrome.
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After launching in 2017 with four players, Cockram has built an entire community for young disabled people - and his inspiring story has now received global attention.
The Penguins are now the subject of a critically-acclaimed film called 'Mighty Penguins', which is premiering at film festivals across the world.
It is an illuminating story about how football can transform lives and give people a sense of belonging.
"The last few months has just been an unbelievable journey," Cockram told talkSPORT. "Louis Myles, the director, got my number from you guys and phoned me up. I thought it was a wind-up!
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"We swore at each other for a few minutes and then I thought, 'This could work'.
"Six months later, it's turned into the most heartwarming, wonderful, beautiful film that I've ever seen. But of course, I'm biased."
He added: "The first time we watched it, me and my wife were flown out to New York to the Robert De Niro Cinema in Tribeca. I'd never seen it.
"It blew us away. We were sitting there with all the Americans and you have to watch it two or three times to take it all in.
"I'm in the film and it's done the Tribeca, it's just done a week in LA in Santa Monica. We had the UK premiere a few weeks ago for friends and family.
"Mark Kermode [well-known film critic], during his live show at the BMI, reviewed the film on stage with some of the cast.
"To watch it is to love it. I didn't want it to become a pity film because that's been done. I just wanted to show how incredible the kids were.
"It's very raw. The parents talk openly and honestly and candidly about the travesties that they have to go through on a daily basis. But it's uplifting and really funny."
With the support of the high-flying Brentford first-team, the Penguins formed a guard of honour at the Gtech Community Stadium for the Premier League clash with Leicester in March.
Cockram's side have also captured the imagination of Bees manager Thomas Frank, who is desperate to organise a screening of the film for his staff.
Their story continues, as well, with Brentford arranging a friendly for the Penguins to face Athletic Bilbao's Down's Syndrome team in Spain.
Cockram added: "Thomas Frank has messaged us and he wants to watch it at Brentford with his staff.
"It ends up with the kids being guard of honour for the Premier League game against Leicester, which was my biggest dream for the kids.
"Brentford and Athletic Bilbao have got together and they're flying us out to play the Down's Syndrome team in October, then our film is being shown in Bilbao Square.
"Brentford have just been amazing and I can't wait for Thomas Frank to see it."
Few footballers reach the heights of playing for Tottenham, especially in the 1980s.
Fewer still can boast about careers in firefighting and business alongside professional football.
But Cockram knows everything pales in significance to his work with the Penguins - because of the way they make him feel.
He continued: "Every kid is on their own timeline, nothing is forced or rushed But the feedback we've had from schools and parents has been through the roof.
"The way they speak to their confidence... it's all about feeling part of a bigger community and not feeling like outsiders anymore."
Cockram added: "I've done a lot in my life but this is the greatest thing I've ever done. It's weird at times, but analysing the film and analysing my life, I get more from the kids than I give to them sometimes.
"I've got broad enough shoulders to be the mouthpiece for these beautiful people."