Britain's Prince William admitted being a parent is "physically and mentally demanding".
His wife, Catherine, Duchess of Cambridge, gave birth to the couple's first son, Prince George, on 22 July and the Duke of Cambridge joked the baby was noisy but "good looking".
Speaking yesterday at the Anglesey Show on the island of Anglesey in north Wales, he said, "She [Kate] and George would have loved to have been here. He's pretty loud ? and of course, extremely good looking.
"I have to say that I thought search-and-rescue duties over Snowdonia were physically and mentally demanding ? but looking after a three-week-old baby is right up there."
The royal couple have lived on the island since January 2010 while William has been based at nearby RAF Valley where he works as a Royal Air Force search-and-rescue pilot.
While he was sad to say goodbye ahead of the couple's move next month, he noted they "look forward" to coming back as a family in the future.
He added, "I know that both of us will miss it terribly when my search-and-rescue tour of duty comes to an end next month, and we have to move elsewhere.
“From the bottom of my heart, thank you for making my wife and me so welcome when we arrived here, as you do thousands of visitors each year.
"This island has been our first home together, and it will always be an immensely special place for us both. Catherine and I look forward to returning again and again over the coming years with our family."