We Do Not Know
The answer by @Praxis uses the source at awoiaf which states:
Mace Tyrell is no more than 10 years older than Cersei Lannister, who was born in 266 AC, indicating that Mace was born in 256 AC. Any later seems unlikely, since that would make Mace's mother Olenna relatively old during the birth of her first son.
Mace was thus born in 256 AC.
Looking into the sources for this we see that Cersei was born in 266 AC:
What Tywin Lannister made of this is not recorded, but in 266 AC, at Casterly Rock, Lady Joanna gave birth to a pair of twins, a girl and a boy, "healthy and beautiful, with hair like beaten gold."
The World of Ice and Fire, The Targaryen Kings: Aerys II
Then Cersei believes Mace is no older than 10 years more than her but this isn't necessarily true (unreliable narrator).
Mace Tyrell was no more than ten years older than Cersei, yet she thought of him as her father's age, not her own. He was not quite so tall as Lord Tywin had been, but elsewise he was bigger, with a thick chest and a gut grown even thicker. His hair was chestnut-colored, but there were specks of white and grey in his beard. His face was often red. "Lord Tywin was a great man, an extraordinary man," he declared ponderously after he had kissed both her cheeks. "We shall never see his like again, I fear."
A Feast for Crows, Cersei II
From Cersei's description and the birth dates it would put Mace to have been born around 8-10 years before Cersei so 258 AC to 256 AC though we don't know exactly when. So although the source for the other answer is reliable it's conclusion is not, the conclusion is simply made as a guesswork and not by looking into the material more.