From The Peerage of England, 1766, available from Googlebooks.
The honour of Duke is hereditary, and he has the title of His Grace. His eldest son (if a Marquis be his second title) is so styled ; and all his other sons and daughters have the title of Lord or Lady joined to their christian names, as Marquis of Tavistock, Lord George Sackville, LadyHarriott Somerset, &c.

The mantle, or surcoat, which he wears at the coronation of a King, or Queen, is of crimson velvet, lined with white taffata, and the mantle is doubled from the neck to below the elbow with ermine, haying four rows of spots on each shoulder : but the robe he wears at his creation, and in parliament, is of a fine scarlet cloth, lined with white taffata, and is doubled with four guards of ermine, at equal distances, with a gold lace above each guard, and is tied up on the left shoulder with A black ribbon.

His cap is of crimson velvet, lined with ermine, having a gold button and tassel on the top : and his coronet, which is also of gold, is set round with flowers, in form of strawberry-leaves.

Dukes are styled by the King, Our right trusty and entirely beloved cousin ; and if of the privy council, then with the addition, and counsellor.

I have been known to poke fun at the number of eligible dukes inhabiting Romanceland, and a survey of the situation in the 1760s, the period of my Malloren World, shows why.

There were an unusual number of dukes of eligible age, but slim pickings for would-be duchesses. Clearly dukes married young, and this fits the period. Important assets were to be protected, no left to chance or whim.

Leaving aside the royal dukes, there were 22 English dukes (I've left out the Scottish ones here), and only six are eligible.

Beaufort, Bolton, Bridgwater, Devonshire, Portland, Kingston, and Somerset.

Beaufort, 21, will marry in 1766
Bolton is 47, odd, perhaps mad, and will shoot himself in 1765.
Bridgwater, 29, is already seen as a confirmed bachelor.
Devonshire is 17.
Portland, 27, will marry in 1766.
Kingston, 54, will marry in 1769.
Somerset, 48, and will never married.

Those who were dukes in their twenties were generally urged into marriage young, including, my fictional one, the Duke of Ithorne. It's easy to see why he was the target of so many ambitious young ladies!

However, it's interesting to see how many were born in the 1730s. It must have formed an interesting "dukes' club" in the mid 18th century.

First I'll list the real one who appears in a couple of my books.
Bridgwater. (That is the correct spelling.) 1736-1803, became duke in 1748 (29 in 1765). He inherited an impoverished title but became rich through his canals, which form part of the plot of Tempting Fortune. He never married, though he's said to have wanted to marry Elizabeth Gunning, when he first husband died in 1758.

Next, in alphabetical order.
Ancaster, became duke 1742, married. His heir b 1756
Beaufort, 1744-1803, became duke in 1756 (21 in 1765) Marries 1766.
Bedford, an older one, 1710-1771. Married.
Bolton, 1718-1765, (47 in 1765) unmarried, (but on 5th July, 1765, he shot himself in his home in Grosvenor Square.
Chandos, became duke 1744, m 1728. Heir b 1731 but m 1753
Cleveland, b 1697, became duke 1730, m 1731
Devonshire, 1748-1811, became duke in 1764, aged 17 in 1765
Dorset, (new one oct 1765, b 1710 and married.)
Dover, elderly, b 1698
Grafton, 1735-1811, (30 in 1765) Married in 1756. Divorced in 1769, then married again.
Kingston, 1711-1773 (54 in 1765) became duke in 1756 m 1769.
Leeds, 1713-1789, became duke 1731, m. 1740, son and heir is only 10
Manchester, 1737-1788, (28 in 1765) Married in 1762
Marlborough, 1738-1812 (27 in 1765) Married in 1762
Montagu. Interestingly, became duke in 1749 ("took the name and arms") through his wife, a co-heir of the Duke of Monagu. His son, Marquess of Monthermer, b 1734.
Newcastle, complicated, but in 1765 the duke was elderly and without issue.
Norfolk, 1686-1777, (79 in 1765) no issue. The heir of the heir presumptive was in his 20s in 1760.
(Northumberland, 1742-1817, (23 in 1765), married in 1764 (This stage of the dukedom only created in 1766))
Portland, 1738-1809 (27 in 1765) married in 1766
Richmond, 1734 -1806, (31 in 1765) became duke in 1750, married 1757 no legitimate issue.
Rutland, 1696-1779, so elderly. His heir is 39 and married, his son is 10.
St. Albans, 1740-1802 (25 in 1765) married in 1763
Somerset,** 1717-1792, (48 in 1765), became duke in 1757, never married.

At race meeting at York in 1770, D of Devonshire, Kingston and Northumberland.
In 1764 the Duke of Grafton's Antonius raced at Newmarket against the Duke of Cumberland's Herod and lost. Total bets of 100,000 pounds rested on the result. Herod won.