A source told The Sun: "Will.i.am loves the food. It makes a change from backstage catering, restaurants and hotels. Cheryl has always been interested in food but recently started taking it seriously. It's a way to unwind."
Meanwhile, a separate insider divulged to Reveal magazine that Cole has offered will.i.am advice on how to appeal to the British public.
The informant said: "She's giving him advice on everything, from his manner to his appearance.
"She told him to cut back on the name-dropping, as it may work in America but it doesn't go down well over here. And she's given him loads of tips on how to adjust his performance for a British audience.
"Cheryl's also suggested that he should show more empathy and not be afraid of showing emotion on the show. And she's delighted with the results."