Unfortunately for Kublai Khan, he was not as feared as his great-grandfather had once been, and Mongolia would eventually begin to break off into civil wars.
In the aftermath, the Mongols retreated back to the steppe, never again playing an important part in history. But the same can't be said of Kublai Khan.
This means that he would have had to have had hundreds of children, and we know that his son Jochi had 40 sons and his grandson Kublai Khan had 22 legitimate sons.