Is Cao Cao’s grandfather really a eunuch

no But he was a eunuch afterwards.
Cao Cao’s father was named Cao Chong, and Cao Chong’s foster father was the eunuch Cao Tengzhi, who served as a eunuch. Cao Cao should have had the surname Xiahou. According to blood relations, his ancestors did not serve as eunuchs.
Cao Cao’s father’s real name was Xiahou Song. Later, Cao Teng, who was appointed as the eunuch at that time, was adopted by the Cao family as his father, so he changed his surname to Cao. In ancient times, a stepson was a son, and a child adopted by someone else was no longer part of one’s own family, just like someone else’s son. Therefore, even the surname was changed to someone else’s.
Like Xiahou Yuan and Xiahou Dun, they were all cousins of the Xiahou family, who were the children of Xiahou Song (i.e. Cao Song)’s own brothers. Cao Hong and Cao Ren are both cousins of Cao Cao in the Cao family, born to the brothers of Cao Teng.
In fact, according to the rules of the Han Dynasty, Cao Cao should not recognize the Xiahou family as his own clan. This was not in line with the rules because he had already been adopted into the Cao family. However, in times of chaos, heroes rise from all directions, and the emperor becomes dispensable, rendering these rules meaningless.
Cao Cao was born into a noble family and was only about 150cm tall. His father, Cao Song, was the adopted son of the Grand Minister of Zhongchang, Qiu Caoteng. The “Records of the Three Kingdoms” recorded that he “could not be judged for his birth and death.” However, some believe that his original surname was Xiahou, and because Cao Song later became Cao Teng’s adopted son, he changed his surname to Cao Shi. There are also claims that he was the son of Cao Tengtang’s brothers. When Cao Cao was young, he was already proficient in both literature and martial arts. The Book of Wei states that he was “extremely talented, shooting birds with his hands, bowing birds and beasts, tasting the southern skin, and shooting pheasants in one day to obtain sixty-three. The Records of the Three Kingdoms states that he was “talented and martial arts genius” and “less alert and powerful”. Due to his misconduct in his youth, no one was optimistic about Cao Cao’s future except for Liang Guoqiao Xuan and Bao Yong from Nanyang, who had been secretly observing Cao Cao. Later, on the recommendation of Qiao Xuan, Cao Cao further developed a close friendship with Xu Shao. One day, when Cao Cao asked himself, “What kind of person is he?” Xu Shao replied, “He is a capable minister in governing the world and a treacherous hero in troubled times.” It is said that after hearing this, Cao Cao laughed heartily.