The first minister has been left "very, very unhappy" after video footage showing one of his son's friends inside Bute House was posted on the internet.
The video showed a man in a dressing gown
The clips on the YouTube website show a young man dancing around in a bedroom wearing a dressing gown.
A spokesman for Jack McConnell said his son Mark did not know that the footage had been taken at the residence more than a year ago.
The short videos, which were only posted this week, have been removed.
The first of the two clips, entitled "Cabby stealing from first minister's house", was posted on Tuesday.
The eight second video shows a young man drinking from a bottle.
A caption with the film reads: "This video features Ewan Macdonald being very sneaky and stealing a shot of vodka from the first minister's official residence (Bute House, Edinburgh) after a day of drunkenness with the big man's son."
The second video, posted on Wednesday, shows the same man dancing around in two different dressing gowns before diving onto a bed.
The 35 second clip is entitled "Cabby in First Minister's House".
The caption says: "Ewan running around like a nutter with the First Minister's dressing gown on in the official residence, Bute House, Edinburgh."
It is understood the short video clips were removed from the YouTube site on Thursday. However, their promos and summaries have remained.
In total, the clips received seven views.
Mr McConnell's son graduated with a degree in American studies from Dundee University in June last year and is now a probationary teacher.
A spokesman for Mr McConnell said: "The video would appear to have been taken in Bute House by friends of the first minister's son."
He added that Mark tried to calm them down several times and has not invited them back since.
The spokesman said: "Mr McConnell's son is familiar with the occasional media interest that comes with having the first minister as your dad.
"It would seem that a couple of his friends are not."