The Queen is "thrilled" at the arrival of her first great-grandson, she told a guest at a Buckingham Palace reception.
Louise Butt said the monarch told her the Duke and Duchess of Cambridge's son, born on Monday, was a "big boy" and that "the first born is very special".
The Queen made the remark during an event for representatives of companies who have been given the Queen's Award for Enterprise.
Mrs Butt, of Bath-based science marketing firm Select Science, said: "She (the Queen) said she is thrilled and she said he is a big boy. She said the first born is very special. We agreed."
It was business as usual for the Queen and other senior royals, hosting the reception for 350 people as her third great-grandchild left hospital with his parents.
The Duke of York, his daughters the Princesses Beatrice and Eugenie, and the Earl and Countess of Wessex joined the monarch for the event celebrating UK firms.
Mr Cable said he had congratulated the Queen on the arrival of her great-grandson, but that she had not dropped any hints about his name during their brief conversation.
"I'm pleasantly surprised she was here but she obviously puts her duties at the forefront of what she does," he said.
He added: "She didn't give any confidential leaks."