The son of a duke inherits the duchy when the duke dies . In the United Kingdom , ducal titles which have been given within the royal family include Duke of Cornwall , Duke of Lancaster , Duke of Clarence , Duke of York , Duke of Gloucester , Duke of Bedford , Duke of Cumberland , Duke of Cambridge , Duke of Rothesay , Duke of Albany , Duke of Ross , Duke of Edinburgh , Duke of Kent , Duke of Sussex , and Duke of Connaught and Strathearn .