The 150 generators which will power the Commonwealth Games were all made at the company's manufacturing base in Dumbarton where in the region of 260 people are employed.
While they are standard pieces of equipment Mr Cockburn, who has been in the interim role for just a few weeks following Rupert Soames' departure to Serco, suggested the workers have been taking additional pride in the assembly and testing processes knowing the kit was going to be on display at such a high profile local event.
He said: "Every generator set produced has its own special branding on it and every one of them was given extra attention as it made its way through the factory.
"All the guys here know every generator providing the power for all the television, the media, broadcast is all going to be coming out of this facility in Dumbarton.
"It means a huge amount for us as a Glasgow company to have the Commonwealth Games here."
Around 150 Aggreko staff will be working on the event which will feature 220 kilometres of cabling deployed across 29 venues.
That will include some stadiums as well as the operations centre, athletes' village and international broadcast centre.
After the games the generators will be deployed wherever the business needs to put them.
Mr Cockburn said: "The kit is designed to work in any application for any customer in any sector anywhere in the world.
"That kit could end up in the Americas, Africa, Asia. Alternatively it might be working offshore Aberdeen or around Glasgow."
Mr Cockburn said he was looking forward to a busy summer of sport.
He joked the football World Cup in Brazil would provide Aggreko with a good training ground for the Commonwealth Games and Ryder Cup.
He said: "We have done a lot of Ryder Cups and we will be providing the power to transmit that around the world.
"We are experienced at golf whether it is the US PGA tour or the European Tour, Asia or Africa or The Open which we have done year-in year-out.
"I'm confident we will do a very good job [at Gleneagles]."
Mr Cockburn was speaking following an event where dozens of local business leaders were invited on a tour of the Aggreko factory at the Lomondgate site in Dumbarton.
Lord Smith of Kelvin, chairman of the Commonwealth Games organising committee, was part of the delegation who took the tour.
Lord Smith said he believes Glasgow is starting to appreciate how big the event will be for the city and suggested around 30,000 contractors will be working during July and August to help businesses of all sizes capitalise on the upswing in visitor numbers into Scotland.
He also said the experience many small firms have undertaken to procure contracts for the Commonwealth Games should hopefully help them to secure further work from major events.
He said: "The Games will help to bolster the Scottish economy, I think by quite a great deal."
After the tour Aggreko revealed a specially commissioned 2014 generator featuring a striking image of a swimmer painted on to it.
That generator will be put on display at a number of Commonwealth locations later this summer.
Mr Cockburn suggested it may start out at Glasgow Green and said a decision with what to do with it after the completion of the event was still to be taken.
Options being considered include putting it on permanent display at the Dumbarton plant or putting it out for rental but at a higher price than other plain generators.
Olympic curler David Murdoch also told the crowd at Dumbarton, which included dozens of orange clad workers from the factory, about the highs and lows from his career including the silver medal he and his crew took home from the Sochi games.