The new largest cruise ship ever built, Icon of the Seas of Royal Caribbean International, has departed Miami on her maiden passenger voyage.

The ship set sail Saturday carrying more than 7,600 passengers and a crew of 2,350, bound for the Caribbean.

Every single cabin on the ship was booked out amid what Royal Caribbean described as “unprecedented” demand, even for a new ship.

Built over the course of 900 days at the Meyer Turku shipyard in Turku, Finland, Icon of the Seas is longer than the Eiffel Tower is tall, but her monumental size, at 250,000 gross tons, is more a result of her width and abundance of passenger decks.

There are 20, and they’re packed with bars, lounges, restaurants, casinos, theatres and of course thousands of cabins, in dozens of varieties and categories.

Up top there are seven swimming pools including a 40,000-gallon “lake,” and six water slides, while down on the promenade there is a carousel, and what Royal Caribbean says is the largest ice arena at sea.

Across the ship there are more than 40 dining venues and bars, and for entertainment there are 50 musicians and comedians as well as a 16-piece orchestra.

The $2 billion Icon of the Seas is the first in Royal Caribbean’s new Icon Class of ships and is powered by what Royal Caribbean says is eco-friendly Liquefied Natural Gas (though some experts say LNG systems can leak damaging amounts of methane gas into the atmosphere).

It also features a system — microwave-assisted pyrolysis — for converting waste to energy-producing gas, and a reverse osmosis system to provide nearly all the fresh water the ship needs.

Icon of the Seas’ maiden voyage comes just a few days after she was christened in style by global footballstar Lionel Messi, now with the Inter Miami side, who pushed a button to send a bottle of Champagne crashing against the ship’s bow.

After leaving her Miami homeport Saturday on a sold-out inaugural cruise, Icon of the Seas will spend a week in the Caribbean before returning to Miami.

At 2,000 feet long (365 meters), she takes the title of world’s largest cruise ship from Royal Caribbean fleet-mate, Wonder of the Seas, which is (just) 230,000 gross tons.