The Prince of Wales shared the snap, featuring a him as a small Royal running around a garden while his father -- looking tall and stylish in a dapper suit -- supervises.

Will's got a huge grin on his face ... and, even his usually stoic dad's cracking a smile -- a rare sight for the King of England. William addressed His Royal Highness informally in the caption, calling him "Pa."

The prince's post comes at the end of a major weekend for the British Royal Family ... who participated in Trooping the Colour -- a celebration of the King's official birthday

The annual ceremony featured all of the Royal regulars -- Charles, Queen Camilla, William, his children ... and, even an appearance from his wife Princess Kate Middleton who made her first public appearance since announcing her cancer diagnosis back in March.

Of course, King Charles also announced his own cancer diagnosis earlier this year ... unclear exactly what type, but he's been strong enough to make a series of public appearances which is always a good sign.

William will one day succeed Charles on the throne, so the two spend quite a bit of time together ... and, it makes sense William's thinking of the good times in light of his dad's illness.

BTW ... a pic of William and his kids was posted on the same official Prince and Princess of Wales account -- so he got his own tribute as well.