Let them eat sugar-free gourmet vegan cake topped with 24-karat gold leaf.

We knew Mayor Bloomberg was stinking rich, frequently clueless and often in Bermuda. But the mayor, whose disastrous third term brought us Snowmageddon, budget bupkis and Cathie Black, has made a move that seems unusually crafty.

To his sextet of sumptuous houses — in Manhattan, Florida, London, Bermuda, Vail, Colo., and Westchester, where his horsewoman daughter hangs out — the bachelor mayor is quietly adding a show-stopping, $20 million-plus Georgian mansion in the Hamptons.

He’s signed a contract on a cute, little shack of 22,000 square feet. Most New Yorkers don’t even go bowling in such monstrous spaces. Bloomberg’s Little House on the Shore in Shinnecock Hills sits on one of the plushest golf courses in the nation and boasts 11 bedrooms, The Post’s Jennifer Gould Keil reported. Bathrooms total eight, with another half-bath thrown in for guests Bloomy doesn’t want spending the night.

An exercise in conspicuous consumption? Or a smart move? The estate features a tree-lined, half-mile approach to discourage paparazzi and former aides. But it may have little to do with Bloomberg forming a buffer from his onetime pal, the vehicularly challenged, fired Schools Chancellor Cathie Black, who hit a bunch of trees as she backed out of a jolly Hamptons party this month.

Bloomberg’s acquisition seems to have everything to do with bypassing a proposed city law.

Last month, to overwhelming support, City Councilman Peter Vallone Jr. introduced legislation — I’ll call it the “Where in the World is Mike?” bill — that would require any mayor who travels more than 250 miles from the city for 24 hours, or who leaves the country for even a minute, to disclose that he’s taking a hike. (He won’t have to tell if he’s going to Washington or Albany, where this year, Bloomberg got humiliated by Gov. Cuomo at budget time.)

Bloomberg is said to be furious over the move, which came about after he was found to be in Bermuda as the post-Christmas blizzard of 2010 bore down on the city. But if the bill passes, and indications are that it will, Bloomberg will have avoided the law by sitting pretty in the Hamptons, which falls within the 250-mile “Where’s Mike?” radius.

“I think it’s fair speculation on our part that he’s anticipating passage of this bill,” said one government source who’s watching the action.

A mayoral spokeswoman won’t comment on the mansion. On the proposed legislation, she was more chatty:

“We’ve said time and time again that the mayor always remains in contact with his senior staff and all relevant parties” when he’s gone.

It didn’t seem that way during the City Council snow hearing earlier this year, as a depressing array of flunkies couldn’t come up with a coherent explanation as to why no one declared a snow emergency — which would have kept traffic off the streets and started the snow plows rolling. Not only was Bloomberg unavailable at the blizzard’s onset, his No. 2, Deputy Mayor Patti Harris, was stuck in Washington. When the mayor emerged, he advised buried New Yorkers to see Broadway plays.

The bill “is not aimed at Mayor Bloomberg,” Vallone told me — as if every mayor flies around in private jets. A mayor wouldn’t even have to tell where he’s going, just who’s in charge.

“The snow storm did make us aware of the fact that sometimes there is a breakdown in communication,” Vallone said. “I’m concerned about another 9/11 situation, planes grounded and no cellphone communications. We may need to know at a moment’s notice who has authority on the streets of New York City.”

But the privacy-freak mayor is smarter than you.

Where in the world is Mike Bloomberg? He may be on a horse trail, picking daisies or perfecting his golf swing. You’ll never know.

Let’s just hope he gets cell service in the notoriously spotty East End.

Hey, three’s a crowd, ya know?

She didn’t get no satisfaction. Goddess/porn star Bree Olson has overshared about her live-in menage a trois with Charlie Sheen and Goddess II, Natalie Kenly: Loved him, hated her, Olson told ABC News.

“I felt like I couldn’t show Charlie the affection and the love that I wanted to show him, because of how she would react,” Olson said. Ah, the typical American family. And they let Sheen raise kids?

Just ride him off

The city’s subway system is broke. Workers, if you can find one awake, are shockingly apathetic. Service is cut, without warning, leaving frazzled passengers scrambling for seats on trains that may, or may not, make it to their destinations on time.

And now, Metropolitan Transportation Authority Chairman and CEO Jay Walder has resigned abruptly, to run a private transit system in Hong Kong.

May he do as fine a job with Asian trains as he did with ours.

Playing court for a fool

Lindsay Lohan has turned a judge into a chump.

After receiving second, third and 42nd chances to clean up her act, the walking time bomb, convicted drunken driver and shoplifter pouted, stamped her feet — then threw a boozy barbecue last month while under house arrest. Last week, LA Judge Stephanie Sautner got peeved once again because La Linz has completed just four of 60 court-mandated days of community service. Linz paraded into court aboard $1,000 Christian Louboutin peep-toes. And her lawyer actually said Linz can’t afford a required shrink.

Doesn’t Saunter get it? Give her an inch, she takes 10 miles. Lock up Lindsay! If she won’t learn, at least she’ll be off the street.

Oh, and you think ‘Shrek’ isn’t dreck?

DreamWorks Animation chief Jeffrey Katzenberg warned revelers at an Aspen, Colo., conference that this year’s crop of movies is utter crap.

“They suck,” he declared. Ya’ think?

“Sex and the City 2” didn’t come out this year, nor did “The Tourist,” or those asinine “Shrek” sequels for which Katzenberg is to blame. Bottom line: Read. It’s not safe in theaters.

Coming back down to earth

“Job well done, America.” With that, Mission Control welcomed the space shuttle Atlantis back to planet Earth last week. For the last time.

I understand why President Obama pulled the plug on a money drain called the space-shuttle program, shifting the heavens to private industry. But when Atlantis touched down, halting our nation’s heavenly aspirations (who knows for how long?), it was a moment of unexpected grief.

“We each got choked up at different times during the mission,” said Atlantis pilot Doug Hurtely, a 44-year-old Marine Corps colonel from upstate New York.

We’ve all grown up with rockets and countdowns, with moonwalks and “The Right Stuff.” And with the idea that Americans will always go faster, farther, higher and better than anyone. Now it’s over.

Job well done.