Sun, 22, the Olympic champion in London last year, equalled Hackett in claiming world titles at 400, 800 and 1,500 metres while 16-year-old Ledecky became only the second woman after Italian world record holder Federica Pellegrini to break four minutes.
The opening day of competition in the specially constructed pool at Barcelona's hilltop Palau Sant Jordi was a triumph for the United States, who also took gold in the women's 4x100 relay and silver in the men's race behind France.
While Sun's three titles in the longer freestyle events have come at two different championships - he won the 800 and 1,500 in Shanghai two years ago and was second in the 400 - he remains on course to repeat Hackett's three golds from the 2005 edition in Montreal.
He led the 400 from the start on Sunday, pulling inexorably away and touching in a time of three minutes 41.59 seconds.
Japanese teenager Kosuke Hagino took silver, more than three seconds behind Sun in 3:44.82, and American Connor Jaeger, 22, won the bronze in 3:44:85.
"In the last year I experienced many things and I still managed to win my gold medal," Sun told reporters.
Ledecky, a gold medallist over 800 metres in London in the first major event of her career, leaped out of the water and punched the air after she secured the first U.S. 400 freestyle gold since Janet Evans in 1991 and smashed the American record by nearly two seconds.
She was initially on course to break Pellegrini's world best of 3:59.15 but slipped off the pace in the final 100 metres to finish in a time of 3:59.82.
"I just got into it, and I'm still in shock over the time," Ledecky told reporters. "I didn't know really how fast I was going but it just shows what happens when you get in a race with the best in the world."
VOCAL SUPPORT
Spain's Melanie Costa Schmid gave the home supporters something to cheer by taking silver in 4:02.47 and Lauren Boyle of New Zealand was third in 4:03.89, the first woman to win a medal for her nation at a world championships.
Olympic champion Camille Muffat of France finished a disappointing seventh.
The popular 4x100 freestyle relay events, bringing the evening's racing to a close, got the crowd on their feet.
The French men were given vocal support from a sizeable contingent of their flag-waving compatriots, who watched their heroes storm from behind to see off the United States, Russia and Australia.
Olympic champions in London last year, France were fourth when Jeremy Stravius dived into the water for the final leg but he hauled in American James Feigen, Russia's Danila Izotov and James Roberts of Australia to touch in three minutes 11.18 seconds.
The United States matched their silver from London in a time of 3:11.42 and Russia pipped Australia to the bronze in 3:11.44.
It was France's first world championship gold in the event and they went one better than the silver they won in Shanghai.
"Our strategy paid off," Fabien Gilot, who swam the third leg, told reporters. "It was like being at home with all the French supporters."
Megan Romano swam a blistering final leg to overhaul Australia's tiring Alicia Coutts and snatch relay gold for the American women and improve on their silver behind Netherlands in Shanghai.
Australia, Olympic champions in London last year, led until the final 50 metres through Cate Campbell, her sister Bronte and Emma McKeon but Romano was too strong for Coutts, who swam in the 100 butterfly and 200 medley semi-finals only hours before the relay final.
Romano came home in 3:32.31, with the Australians finishing in 3:32.43 and the Netherlands, who pipped the U.S. to silver in London, were third in 3:35.77.
(Editing by John Mehaffey)
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