Contrary to some claims here, it's not the taxpayer, who doesn't support the royals.
The monarchy is supported by a minority percentage of the Crown Estate income, in a deal originally made in the late 18th century. This percentage is paid to the Queen and is used to cover her general expenses as monarch -- staff salaries, for example. The majority percentage goes to the state, meaning the taxpayer. A couple of years ago, that majority percentage amounted to around 280 million pounds.
The Queen herself pays annuities, out of her personal wealth, to a number of those royals who carry out royal engagements and handle other duties. These people include Princess Anne, the Wessexes, and the Gloucesters. However, Prince Charles pays the official expenses of the Cambridges and Prince Harry out of his Cornwall income. The Cornwall Duchy has been a official appurtenance of the eldest son of the monarch since the 14th century.
All the other Cambridge expenses must be covered by them. Prince William is wealthy in his own right, and his wife is the child of rich parents. I've no doubt they established trust funds for all three of the Middleton children some time ago.
The only real taxpayer expense is security coverage, which runs to about 100 million pounds per year, according to the most recent figure I've seen. However, the majority percentage of the CE income that the state gets more than compensates for that. The taxpayer is actually getting the better end of the deal there.
It is possible that George's education is considered an "official" expense, so that the fees would be paid by the Duchy of Cornwall rather than by the Cambridges themselves.