The birth of that which became the Roman Empire of antiquity is part and parcel of myth, legend, fact, and conjecture.
The two primary stories surrounding the founding of Rome entail the twins Romulus and Remus who were nursed by a she wolf and the refugee of Troy, Aeneas, who was the subject of the epic by Virgil called The Aeneid and his issue, a son named Ascanius aka Iulus for whom the Julio-Claudian dynasty was named.
The stuff of legend, those mythological references to Ancient Rome being founded by the two demi-god brothers named Romulus and Remus on 21 April 753 BCE remains one of the most compelling and interesting sidebars for a child such as myself learning of these things at an elementary school age.
Included in this legend is the claim that Romulus killed Remus during the course of an argument regarding who would rule the city (or where the city would be located) and named the city Rome after himself.
Not having been a big fan of Virgil, the second Aeneid based story was one I never really pursued.
Though the year of the founding of the city varies between 752 and 728 BC ... the day has been steadily fixed April 21 by all of the individuals involved in determination of the date; which is the date of the feast of Pales, godess of shepherds and livestock. Incidentally, the Roman calendar actually began at 753 BC.
So it really doesn't matter which year to which you might subscribe as that of the founding of Rome. Today marks the anniversary so — Happy Birthday Roma !