A second added: "So adorable. Looks like Kate's dad."
A third chimed in: "A little dote - the image of his Grandpa Middleton!"
Among the cute snaps shared by the Duke and Duchess of Cambridge was one that shows the cheeky little prince grinning for the camera while wearing a spotless blue gingham shirt.
A follow-up photo shows the prince giggling while showing off his rainbow-coloured hands, while another pic shows his brightly painted handiwork.
The royal husband and wife later took to Instagram to share their first Instagram versus reality photo, featuring the mini royal.
Louis and his siblings, Prince George, six, and Princess Charlotte, four, are currently isolating at their country home, Anmer Hall, in Norfolk.