The official announcement has been made.
Prince William has been created as Duke of Cambridge, Earrl of Strathearn and Baron Carrickfergus. According to the 1917 Letters Patent, William's eldest son will be HRH and Prince during the Queen's lifetime. All other children will be styled as the as children of a duke. This will change when Charles succeeds to the throne. However, the queen could change this to allow all the children to be royal.