The Spanish Government wanted to profit from Cuba as much as possible. In the end of the 17th century, piracy became less common and things developed more easily.
The Spanish Crown completely owned the tobacco industry, which prompted a rebellion from tobacco growers. Spain put this down, and set up a company to control all Cuban trade.
In 1762, the English took Havana. They allowed trade with the rest of the world. Slave imports and prosperity for Cuba both increased greatly.
The English traded Cuba for Florida to the Spanish. The Spanish were then pressured to allow free trade, and the country remained wealthy.
Sugar became more important. It beat tobacco as the most important crop, and the Revolution in Haiti brought an end to competition with that nation.
Havana grew with Cuba's prosperity. It became a huge city for the times, and in 1728, gained a university. A postal service was created in 1764 and a newspaper in 1763. In 1790, the city gained lamps in the streets.
The major difference between Cuba and other Spanish colonies during this time was that Cuba's economic production largely remained on the island and was put towards developing it, rather than being returned to Spain.