This is a German Army M-18 "ear cut-out" helmet from the World War I period (1914-1918), that was reissued for World War II (1939-1945).  Several layers of paint can be seen on the outside of the helmet, evidence that it was called back into service.  The M-31 liner in the helmet is also non-original for this model helmet, indicating that a new liner was inserted when it was reissued.1 

There is a German Heer (Army) eagle insignia on the left side of the helmet, which is turning gold due to aging lacquer.  On the right side of the helmet is the German national tricolor (black/white/red).  It appears the army eagle is placed over the slate gray reissued paint while the tricolor shield is applied below the paint, which is only visible due to the paint chipping. This adheres to the army bulletin issued in March 1940 to remove or camouflage the tricolor shield.2 On the neck guard in permanent ink is the word "Rambo," likely added after the war.

Germany World War I
Infantry Helmet 1918
HRH-144-0410

Description by Joe Woodward