Alaric and goths
The Gauls sacked and destroyed the city of Rome in 476.
rome
In 410 the Visigoths (Goths of the west) sacked the city of Rome. They did not destroy it.
Rome was sacked by the Visigoths in 410 and by the Vandals in 455.
vandals and visigothes
If you are referring to the city of Rome, as opposed to the Roman Empire, three Germanic peopled sacked Rome. The Visigoths in 410, the Vandals in 455 and the Ostrogoths in 546.
Although Rome was sacked 3 times in antiquity and 4 times in the middle ages, it was never captured.
No one sacked Rome during the Punic Wars.
The barbarians who conquered Rome were called the Goths.
Alaric I did not actually capture Rome. He sacked the city and left before the Roman army form garrisons around the empire would catch up with him. The sack was a shock because Rome had not been sacked for 700 years. It also showed that Rome was vulnerable.
The city of Rome was first conquered by foreign invaders in 410 AD, when the Visigoths, led by King Alaric, sacked the city. It was then again conquered in 455 AD by the Vandals, led by King Gaiseric.
No one sacked Rome in 476 BC. Rome was sacked by the Senone Gauls in 390 BC