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In one touching image, three-year-old Princess Charlotte is kissing her sleeping brother, while the other shows the royal baby propped against a cushion.
The image with Princess Charlotte was taken on May 2 -- her third birthday -- while the other, in which Louis wears a white jumper and trousers, was taken on April 26, three days after he was born.
He will hold the title of prince after the Queen changed the rules in 2012 to ensure that all of William's children would be entitled to the style, not just his eldest son.
The birth kicks off a busy summer of royal celebrations, with Prince Harry set to marry US actress Meghan Markle on May 19.