Gaspar de Ávalos de la Cueva
Gaspar de Ávalos de la Cueva( 1485 – 1545), also named Gaspar Dávalos de la Cueva, was a Spanish Roman Catholic bishop and cardinal.
Francisco Fernández de la Cueva, 4th Duke of Alburquerque
Francisco Fernández de la Cueva y Girón, 4th Duke of Alburquerque( in full)( c. 1510 – 1563) was a Spanish nobleman.
He was the son of Don Beltrán de la Cueva, 3rd Duke of Alburquerque and of Doña Isabel Girón.
He fought in Africa and participated in the siege at La Goletta and the Conquest of Tunis in 1535.
He married Doña Constanza de Leiva, daughter of the principe di Ascoli, and later( 1549) Doña María Fernández de la Córdoba, daughter of Luis Fernández de Córdoba, 2nd Marquis of Comares.
Beltrán de la Cueva, 3rd Duke of Alburquerque
Beltrán de la Cueva y Toledo, 3rd Duke of Alburquerque, (in full), (c. 1478 - 11 February 1560) was a Spanish nobleman and military leader.
He was born in Cuéllar, the son of Don Francisco Fernández de la Cueva, 2nd Duke of Alburquerque and of Francisca de Toledo, daughter of García Álvarez de Toledo, 1st Duke of Alba.
Beltrán de la Cueva was appointed captain general of the Spanish Army, and commander-in-chief of the English Army in France (under queen Mary I of England).
He was named a Knight of the Order of the Golden Fleece in 1531, a Viceroy of Aragon in 1535, and a Viceroy of Navarre in 1552, position he held until his death in 1560.
Francisco Fernández de la Cueva, 10th Duke of Alburquerque
Francisco V Fernández de la Cueva y Fernández de la Cueva,( Genoa, Italy, 17 November 1666 – Madrid, Spain, 28 June 1724) was the 10th Duke of Alburquerque, a Grandee of Spain, a Knight of the Order of the Golden Fleece since 1707, and Viceroy of New Spain from 27 November 1702 to 14 January 1711.
His tenure as Viceroy of New Spain is commemorated in the namesake of Albuquerque, New Mexico.
He was the nephew of Francisco IV Fernández de la Cueva – Colonna,(* Barcelona, 1618/ 1619 – † Madrid( Palacio Real) 27 March 1676), 8th Duque de Alburquerque and many other lesser titles, also a Viceroy of New Spain,( 1653 – 1660), and Viceroy of Sicily,( 1667 – 1670), and the son of the 9th Duke of Albuquerque, and many other lesser titles, the cadet brother of the 8th Duke, and inheritor of the titles, Melchor Fernández de la Cueva(* Madrid, 2 March 1625 – † Madrid 12 October 1686).
His father, Melchor, the 9th Duke, had married in 1665 his niece Ana Rosolea Fernández de la Cueva, the 3rd Marchioness of Cadreita, Navarre, daughter of the 8th Duke of Albuquerque Francisco IV Fernández de la Cueva and Juana Francisca Díez de Aux y Armendáriz, herself daughter of Lope Díez de Armendáriz, Viceroy of Mexico( 1635 – 1640).
This Spanish – Equatorian, Francisco Fernández de La Cueva y Fernandez de la Cueva, 10th Duke, was thus family connected through paternal and maternal links with 2 former Viceroys of New Spain, Viceroys of México, his uncle Francisco IV, the 8th Duke of Albuquerque and Lope Díez de Armendáriz.
He was captain general of the Kingdom of Granada and captain general of the coast of Andalusia.
Beltrán de la Cueva, 1st Duke of Alburquerque
Beltrán de la Cueva y Alfonso de Mercado, 1st Duke of Alburquerque( c. 1443 – 1 November 1492) was a Spanish nobleman who is said to have fathered Joan, the daughter of Henry IV of Castile's wife Joan of Portugal.
His alleged daughter, called" la Beltraneja", was deprived of the crown of Castile because of the uncertainty regarding her parentage.
Beatrice, Countess of Alburquerque
Beatrice of Portugal was Countess of Alburquerque as the wife of Sancho Alfonso of Alburquerque.
She was the daughter of Peter I of Portugal and his wife Inês de Castro.
Francisco Fernández de la Cueva, 7th Duke of Alburquerque
Francisco Fernández de la Cueva y de la Cueva, 7th Duke of Alburquerque( in full)( Cuéllar, 1575 – Madrid, 18 July 1637) was a Spanish nobleman, military and politician.
He was the son of Don Beltrán III de la Cueva y Castilla, 6th Duke of Alburquerque and Isabel de la Cueva y Córdoba.
In 1617, he was appointed Viceroy of Catalonia, a function in which he became known as" one of the toughest, most rigorous, and successful of the viceroys of Catalonia ... and had specialized in the suppression of disorder."
To suppress" banditism", he did n't hesitate to clash with the local authority, the Principality of Catalonia, and to restrict the Catalan constitution.
Between 1627 and 1632, he was Viceroy of Sicily, where he had 2 bronze statues erected of Kings Charles I and Philip IV.
He was also a member of the Spanish Council of State and the War Council under King Philip IV.
He served as Ambassador to the Holy See and finally was President of the Council of Italy and Council of Aragon.
Francisco Fernández de la Cueva, 2nd Duke of Alburquerque
Francisco Fernández de la Cueva, 2nd Duke of Alburquerque (in full)
(25 August 1467 – 4 June 1526) was a Spanish nobleman.
He was the son of Don Beltrán de la Cueva, 1st Duke of Alburquerque, by first wife Doña Mencía Hurtado de Mendoza y Luna.
He served the Catholic Monarchs Isabella I of Castile and Ferdinand V of Castile in the Wars of Granada along with his father.
He was the 644th Knight of the Order of the Golden Fleece.
He married before January 1485 Dona Francisca Alvarez de Toledo, daughter of García Álvarez de Toledo, 1st Duke of Alba and sister of his first stepmother, and among two other sons and two other daughters he had the oldest daughter Dona Mencía de la Cueva y Alvarez de Toledo, who married as his second wife Don Pedro Fajardo y Chacón Manrique de Lara, 1st Marquess of los Vélez.
He was the paternal grandfather of the 1st Marquess of Cuéllar in 1562, Don Francisco de la Cueva y Téllez-Girón, Alvarez de Toledo y de la Vega.
Beltrán Alfonso Osorio, 18th duke of Alburquerque
Beltrán Alfonso Osorio y Díez de Rivera, 18th Duke of Alburquerque( 15 December 1918 – 8 February 1994), was a Grandee of Spain and an amateur jockey.
As a Spanish aristocrat, he was known as the" Iron Duke" of Alburquerque.
He was also Duke of Algete, Marquis of Alcañices, los Balbases, Cadreita, Cuéllar, Cullera, and Montaos, Count of Fuensaldaña, Grajal, Huelma, Ledesma, la Torre, Villanueva de Cañedo, and Villaumbrosa.
His son, Juan Miguel Osorio y Bertrán de Lis( b. 1958), is the current Duke of Alburquerque and Duke of Algete.
Baltasar de la Cueva, Count of Castellar
Don Baltasar de la Cueva y Enríquez de Cabrera," iure uxoris" Count of Castellar and Marquis of Malagón( sometimes" Baltasar de la Cueva Enríquez de Cabrera y Arias de Saavedra")( 1626 in Madrid – April 2, 1686) was viceroy of Peru from August 15, 1674 to July 7, 1678.
He was a younger son of the 7th Duke of Alburquerque, and brother of Francisco Fernández de la Cueva, 8th Duke of Alburquerque, who served as Viceroy of New Spain.
He married Teresa María Arias de Saavedra, 7th Countess of Castellar.

Question: Who is Beltrán De La Cueva, 3Rd Duke Of Alburquerque's paternal grandfather?
Answer: Beltrán de la Cueva, 1st Duke of Alburquerque