McCartney happily obliged - and even swapped seats with Corden as they harmonized on some of The Beatles' greatest hits, including "Drive My Car" and "Blackbird". McCartney then recalled the remarkable circumstances under which he penned the Beatles classic "Let It Be", the title track to their final album.
"That's been one of the odd things", McCartney, around the five-minute mark in the video up top, told Corden of the lasting impact of the Beatles' message. "I can remember my granddad, who's a musician, and my dad sitting me down and saying, "We're going to play you the best song you've ever heard".
Paul McCartney joined Corden for a very special installment of the segment, in which the two spent a day driving around Liverpool and exploring the city of McCartney's youth.
As they look around, Sir Paul says one of the downstairs rooms is where "me and John would often come to rehearse or to write".
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Grohl went on to tell a story about a time he attended a party at McCartney's house.
After teasing the first song he ever wrote, the rather catchy "I Lost My Little Girl", McCartney set course for a trip down memory lane - as well as the actual Penny Lane, which they completed with a rendition of "Penny Lane".
"I got a fucking text from him [the next day]", he said. "If my grandad was here right now, he'd get an absolute kick out of this".
The singer revealed that the band thought their music would only last 10 years and expressed his shock at its continued endurance.