Final answer:
The Colosseum, or Flavian Amphitheatre, is the major public work in Rome not constructed during Augustus' rule, as it was built between 70-80 CE, well after his reign which ended in 14 CE.
Step-by-step explanation:
The major public work in Rome not effected during Augustus' rule is the Colosseum, also known as the Flavian Amphitheatre. The Colosseum was constructed between 70-80 CE under Emperor Vespasian and his sons Titus and Domitian, who were members of the Flavian dynasty. This timeline places the construction well after Augustus' reign, which ended in 14 CE. Meanwhile, the Ara Pacis, an altar dedicated to Pax, the Roman goddess of peace, was indeed created at the time of Augustus, specifically on July 4, 13 BCE, being dedicated on January 30, 9 BCE. Other structures like the Theater of Marcellus, the Pantheon (rededicated circa 125 CE but originally built by Agrippa during Augustus' rule), the Ara Pacis, and the Baths of Agrippa were also realized under the influence of Augustus.