Most unlikely that William receives the Dukedom of Cambridge
It really is most unlikely that Prince William will become Duke of Cambridge.
When his father assumes the kingship, he will automatically become:
His Royal Highness
The Prince William
Prince of the United Kingdom of Great Britain and Northern Ireland,
Earl of Chester,
Duke of Cornwall,
Duke of Rothesay,
Earl of Carrick,
Baron of Renfrew,
Lord of the Isles
and
Prince and Great Steward of Scotland.
And at a later stage, when it pleases his father, he will be created
Prince of Wales as well.
So it is most unlikely that Prince William will receive the Dukedom of Cambridge.
Earl of Chester
The earldom was created by William the Conqueror, with the intention of the Earl keeping an eye on any war-like activities by the Welsh. It reverted to the Crown in 1237, and was passed to the future Edward I. He conferred the earldom on his son, Edward II, and since then the Earldom of Chester has gone to every Prince of Wales.
Duke of Cornwall
The Prince became Duke of Cornwall automatically upon The Queen's accession on 6th February, 1952.
The Duchy of Cornwall - the oldest and one of the biggest landed estates in England - has existed for more than 650 years and provides an income for the male heir to the throne.
Duke of Rothesay
When The Prince of Wales is in Scotland, he is known by this title of the Scottish peerage, first conferred by Robert III, King of Scots, on his son David in 1398. An act of the Scottish Parliament in 1469 confirmed its restriction to the heir apparent to the throne of Scotland. Since the 1603 Union of the Crowns the title has descended alongside the Dukedom of Cornwall, and The Prince became Duke of Rothesay at the time of The Queen's accession.
Earl of Carrick and Baron of Renfrew
Other titles of the Scottish peerage inherited by the heir to the throne under the 1469 Act.
Lord of The Isles
This ancient title, held by those who ruled the Western Isles as vassals of the King of Scotland, was annexed to the Crown by James V of Scotland in 1540, to be passed to his heirs.
Prince and Great Steward of Scotland
The hereditary office of Great (or High) Steward dates from the 12th Century. The 1469 Act confirmed that the title should go to "the first-born prince of the King of Scots for ever".