Don Francisco Fernández de la Cueva was born in Barcelona into one of the most aristocratic families of Spain, as the eldest surviving son from the third marriage of his father, Francisco Fernández de la Cueva, 7th Duke of Alburquerque. His father was "one of the toughest, most rigorous, and successful of the viceroys of Catalonia...and had specialized in suppression of disorder." His father's first marriage to Doña Antonia, from the powerful House "de Toledo-Beaumont", was childless. He married again with Ana María de Padilla who deceased before 1614. Their only son, Beltran, died at age 17 in December 1617. In his 3rd marriage, the Duke married Ana Enríquez de Cabrera y Colonna and had 9 children; his wife survived him some 21 years. Francisco, the eldest son, entered military service when very young. He served in the cavalry in Flanders. Later, as general of cavalry, he fought in the defense of Tortosa and in the siege of Barcelona in 1650. One feature of his career would be also his Ambassadorial activities in the Germanic countries.
He made his formal entry into Mexico City to take up the reins of government on August 15, 1653. He was accompanied by his wife, Juana de Armendáriz, the daughter of Lope Díez de Armendáriz, a previous viceroy of New Spain. Because of the war with England, he feared an invasion of Spanish territories in the New World. Because of this he strengthened the defenses of Veracruz and San Juan de Ulúa on the east coast of New Spain. He also sent arms and munitions to Jamaica, Cuba and Florida. He increased trade with the Philippines, Siam and Cochinchina, sending mercury, saltpeter and other mineral products. He ordered the resumption of the minting of gold coins. He collected the royal rents with care, and sent back to Spain large quantities of silver. He reinforced the Armada de Barlovento, which guarded the coast and shipping. He ordered the construction in Campeche of new ships for the coastal and overseas trade. He also repaired the aqueduct supplying Mexico City with water. The viceroy accelerated the construction of the new cathedral of Mexico City, visiting it every afternoon, climbing the scaffolding, and giving monetary rewards to the workers. During a visit to the cathedral on 12 March 1660, a 19-year-old soldier in the viceroy's guard, Manuel Ledesma y Robles of Madrid, attacked the viceroy with a sword. The viceroy survived. Justice was swift for his attacker, who was quickly tried, then dragged around the city and back to the Plaza Mayor, where he was hanged the next day. The city ofAlburquerque, in what is now New Mexico, was founded on February 7, 1706 under his son's direction. He granted land to more than 100 Spanish families there. The writers of this period attributed to his government a strong encouragement for the development of the sciences and the arts. His palace was considered a model of elegance and good taste.
Francisco Fernández de la Cueva married in 1645 Juana Francisca de Díez de Aux Armendáriz and had only 1 daughter. This daughter, Ana de la Cueva y Díez de Aux Armendáriz, was married to her father's younger brother Melchor, thus making him 9th Duke of Alburquerque after Francisco's death.