It's not clear when this was called "blackout." Perhaps it was sold as "chocolate layer cake" for some time before the name was thought of (probably in the 1940s during wartime blackouts).
Steve's Ice Cream in Brooklyn makes a flavor called "Brooklyn Blackout."
Welcome to Brooklyn
What ever happened to Ebinger's Bakery?
Ebinger Baking Company, with a chain of stores across the boro, was founded in 1898 by George and Catherine Ebinger. Famous for their cakes and pies, and especially their Blackout Cake, they closed in bankruptcy on August 26, 1972.
There have been attempts to revive the bakery brand under that name, but none, so far, have been successful.
Named for wartime blackouts, their famous and beloved chocolate-pudding-filled Blackout Cake was a chocolate layer cake filled and frosted with dark fudge and dusted with chocolate cake crumbs that was so popular that other bakeries in the borough, like SeaLane, produced inferior knock-offs.
14 May 1942, Maryville (MO) Daily Forum, pg. 3:
BLACK-OUT CAKES.... 35c
The VAVRA BAKERS
THE SOUTH SIDE BAKERY
4 September 1945, Wisconsin Rapids Daily Tribune, "In Hollywood" by Erskine Johnson, pg. 8, col. 4:
Before leaving New York, Carl Post met SUsan Hayward and asked her if there was anything he could do for her in the big city. "Yes," said Susan, mouth watering, "bring back a chocolate layer cake from Ebinger's Bakery in Brooklyn." Post brought the cake and started back to Hollywood by plane. But the temptation was too great. He ate the last piece over Salt Lake City.
10 November 1961, New York Times, pg. 40:
Ebinger's Bakery Started in 1898,
With German Pastry as a Specialty
It might be said that Ebinger's grew up with Brooklyn. Arthur Ebinger's parents, who has come here from Germany, opened their first Brooklyn bakery on Flatbush Avenue in 1898.
Chocolate cakes, incidentally, are on of Ebinger's best sellers in stores patronized largely by Jewish people.
4 December 1968, New York Times, pg. 43:
(Waldbaum's supermarket ad--ed.)
27 August 1972, New York Times, pg. 19:
Tears Replace the Coffee Cakes
On Ebinger Bakeries Final Day
30 August 1987, New York Times, pg. L.I.31:
You bought a blackout cake: a rich chocolate layer cake filled and frosted with dark fudge and dusted with chocolate cake crumbs. It was named for the wartime blackouts (but, if it had been fed to the enemy, it could have ended World War II two years earlier).
10 July 1991, New York Times, pg. C10:
"Ebinger's is back!" I cried.
...she always brought a stack of green and brown boxes from a wonderful bakery called Ebinger's.
Inside one of those boxes was always a blackout cake.