Movie mistake: a WRONG SONG 'Oj Kozaro'!
The story takes place on the Eastern front, in Russia, however it was filmed in the former Socialist Federal Republic of Yugoslavia (since it was a non-aligned and more liberal communist country, many american or british movies were shot there, like "Force 10 from Navarone" for example).
Now, there's a scene in "Cross of Iron" where the soviet soldiers are singing "Oj Kozaro" (Hey Kozara), a famous Yugoslav WWII partisan song, which the Red Army soldiers didn't know. The song is completely unknown in the ex-USSR, it has a folk melody typical for the ex-Yugoslav countries. It can be found on youtube in various versions.
Kozara is a mountain in Bosnia, where the Axis operation "West-Bosnien" took place in 1942 against Josip Broz Tito's partisans (if you are interested you can check the Yugoslav war film "Kozara" (1962): http://www.imdb.com/title/tt0055059/ )
The Yugoslav background actors in "Cross of Iron" probably didn't know any russian songs and the director though that nobody would notice "Kozara" :)
I find this a little bit annoying, it spoils the feel of authencity of this, otherwise, masterpiece of a war drama.