Mantua is the ancestral city where the male line of the Gonzaga dynasty ruled, first as marquesses, then after 1540 as dukes, in vassalage to the Holy Roman Empire. Monferrato was a duchy since 1574 on the eastern side of Piedmont, and an Imperial fief since the eleventh or twelfth century. The Gonzagas had enlarged their realm with Monferrato after receiving it in dowry from the wife of duke Frederick II Gonzaga. On 22 September 1612, Francis IV, Duke of Mantua and Monferrato died at the age of 26. His death occurred only a couple of months after the death of his father Vincent I, Duke of Mantua. He left only a three-year-old daughter, Maria of Mantua. Francis IV also had two younger brothers who, both being cardinals, could not marry and were thus ineligible to succeed to Mantua's throne. Nonetheless, Francis' two brothers, Ferdinando I  and Vincenzo II , eventually did become Dukes of Mantua. Despite marrying, following the resignation of Ferdinando and the expulsion of Vincenzo from the Sacred College of Cardinals, neither produced any legitimate children. A crisis erupted when Vincenzo II died on 26 December 1627 at the age of 33, the same day that his niece Maria Gonzaga's marriage with Charles de Nevers was celebrated. Nevers was the eldest son and heir of Charles, Duke of Nevers, Rethel and Mayenne. Moreover, he was the head of the cadet branch of the House of Gonzaga, and after Vincenzo II, heir male of the Duchy of Mantua.
Question: Who never produced any children?
Answer: Ferdinando I and Vincenzo II