Australia picked up their first 50-overs title in 1987 before winning three in a row from 1999 to 2007. They picked up a fifth crown when they co-hosted the 2015 event with New Zealand.
"I think we had a really strong run in the early 2000s," Cummins told reporters on Wednesday.
"I think one-day cricket is a format that's really suited Australian teams of the past - not only taking the game on with the batting and having some good quick bowlers, but even in the field ... They were amazing, really athletic.
"Hopefully we can carry it on. It's a pretty good history we've had in World Cups. So hopefully another one."
With their fiery attack, formidable batting and electric fielding, Australia set the benchmark in 50-overs cricket during that era but reigning champions England have replaced them as the dominant limited-overs side, also winning the T20 World Cup in Australia last year.
Cummins, in his first World Cup as Australia captain, is one of several frontline players returning from injuries but he says Australia have what it takes to win in India -- an abundance of all-rounders.
Australia have packed five of them into their 15-strong squad, including an in-form Mitchell Marsh, who is likely to be David Warner's opening partner in the tournament until Travis Head recovers from a fractured hand.
"We've played plenty of games over in South Africa, against India and even these warm-up games. It feels like it's all come together in the last week or so," Cummins said.
"I think in ODI, you need a few all-rounders. And yeah, I feel pretty happy with where everyone's placed at the moment."
Australia will begin their World Cup campaign against hosts India in Chennai on Sunday.
