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As a delivery driver for an upscale bakery favored by celebrity lifestyle gurus, David Lliviganay had access to a warehouse full of some of the most coveted — and costly — cakes in New York City.

The bakery, Lady M Confections, a patisserie with locations around the world, is renowned for its Instagram-friendly Mille Crêpes cake, an elegant stack of about 20 crepes slathered with fluffy cream and topped with a layer of caramelized sugar.

A nine-inch cake can sell for up to $90 — or less when stolen and resold.

The authorities have accused Mr. Lliviganay of doing just that. Earlier this year he was charged with 15 counts of petty larceny, a misdemeanor, and pleaded guilty in July, according to court records.

But a new civil lawsuit filed last week in Queens by the owners of the bakery detailed the full scope of the alleged heist.