The royal couple had met Zakwan Anuar and his mother, Norizan Sulong, at a hospice in Kuala Lumpur, Malaysia. Doctors had expected him to die within 48 hours of their meeting, but his 15-minute chat with the Duchess gave him the strength to battle on for two more weeks, The Sun reported.
The royals were informed about Zakwan's death last night.
"The Duke and Duchess of Cambridge are saddened to hear of Zakwan's death. Their thoughts are with his family," a St James's Palace spokeswoman, said.
Kate was compared to the late Princess Diana after her emotional meeting with Zakwan.
She tenderly laid a hand on his cheek and said: "Are you in pain? You're a brave boy".
Before the visit, Zakwan spent his days asleep or crying with pain. But his face lit up when he saw Kate. He grinned and told her she was "very pretty" as she signed his birthday card.
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She said he was "very handsome".
Sulong, said the "overwhelming" encounter lifted Zakwan's spirits.
"I hope William and Kate will have beautiful and healthy children of their own one day," she added.