The closest thing I found is a song by rebelling/deserting German soldier in the closing days of WWI.
It’s all a Swindle:
The War is for the Wealthy,
The Middle Class must give way.
The People provide the corpses.
This was published in a paper by Nick Howard on the German uprisings of 1918 (collected in a 1999 CUP volume, p. 14). The same song was published (more recently) in a Socialist Review article.
It's not too clear how much this was influenced by Lenin's somewhat similar proclamations, e.g. in "The Tasks of Revolutionary Social Democracy in the European War" (1914):
the necessity of using weapons not against one’s own brothers, the hired slaves of other countries, but against the reactionary and bourgeois governments and parties of all nations
even though that doesn't talk about profit. Separately, Lenin said in his May Day speech (1915)
"War is a “terrible” thing? Yes. But it is a terribly profitable thing."
I guess Sartre should get a mention here for saying it more concisely (although not as precisely) in The Devil and the Good Lord (1951):
When the rich wage war, it's the poor who die.
And as "the rich man's war and poor man's fight" it goes back to the US civil war.
To answer @gerrit's request for the German original of the song; it's given in R. Bessel, Germany After the First World War (Oxford, 1993, p. 1)"
Es ist alles Schwindel:
Der Krieg ist für die Reichen,
Der Mittelstand muß weichen,
Das Volk, das stellt die Leichen.
A bit more searching finds a book in German: H.C.Grünefeld "Die Revolution marschiert: 1806 - 1930" with a several songs on the same theme (around p. 341 in vol 2)