In his memoirs (text in Russian), Marshal Aleksandr Vasilevsky claims the following (emphasis added by me):
I will note in passing that in terms of munitions consumption the East Prussian operation had no equal in the history of wars. The two fronts received 13.3 million shells, 620 million bullets and 2.2 million hand-grenades. During the 13-14 of January alone, the troops of the 3rd Belorussian front consumed over 1000 railcars of munitions, while 2nd Belorussian used 950 cars on the 14th. Altogether, both fronts received 15,000 railcars of munitions. For their transfer from the railcars to the troops (via 2.5 tonne road vehicles), approximately 100,000 automobiles were required.
Is it possible to substantiate this claim? Of course, the quote does not precisely define what length of time is meant by the "operation", nor the exact tonnage (it is unclear what is meant by the 100k trucks) or caliber of the shells.
My immediate thoughts would be to compare this with the great barrages of WWI, when according to Wikipedia for example, 2 million shells were used in about a week by each side at Verdun and similar numbers at the Somme. In WWII, El Alamein seems too small to compare and I can't find aggregate numbers for total tank/shore bombardment/close air support during Overlord. Presumably Vasilevsky was able to discount other Soviet operations in Eastern/Northern Europe, Manchuria and possibly also those of Tsarist Russia as surpassing East Prussia.
edit: I had initially neglected, and a commenter pointed out, that Operation Rolling Thunder (complete by the time Vasilevsky wrote his memoirs in 1978) would almost certainly have exceeded the total tonnage. This also raises the question of whether the Marshal meant sum or the rate of consumption.