In Act 5, Scene 1, Line 73 of Julius Caesar, Cassius tells Messala, "This is my birthday, as this very day was Cassius born." What is the significance of this quote? Why did Brutus say it's his birthday?
There is probably no special significance to Cassius's reflection that this is his birthday. Shakespeare was drawing on Plutarch's lives of Caesar. Brutus, and Mark Antony for his play. He frequently inserted little comments from Plutarch directly into his script just to capture the feeling of the time period. According to the "Introduction" to Julius Caesar in The Pelican Shakespeare:
Never before has he relied so heavily on one source--in this case, Thomas North's 1579 translation of Jacques Amyot's 1559 French version of a Latin translation of Plutarch's Lives of the Noble Grecians and Romans. . . . At certain junctures, the playwright turns North's prose directly into iambic pentameter, barely changing a word.
The effect of Shakespeare's play, even though it is written in English and in iambic pentameter, is to carry the viewer back in time to ancient Rome. Shakespeare creates an hypnotic spell. The viewer becomes a time traveler. Most modern readers' impression of the characters and events connected with Caesar's assassination and its aftermath are derived from Shakespeare rather than from history books. This includes Mark Antony's famous funeral oration, which is probably nothing like what the real Mark Antony said to the mob but seems somehow to be what he should have said.
Plutarch probably quoted Cassius as saying that it was his birthday because Plutarch was that kind of conscientious historian. His "Lives" are full of little details which he picked up from his reading, or from other scholars, or from hearsay. Shakespeare, of course, had to invent most of the dialogue, but he was probably happy to find in Plutarch a line or two of dialogue which he could incorporate verbatim into one of his plays.