  Super star cluster (SSC) A1 (3.1E5 Msun) in NGC 3125 has one of the strongest
(EW = 4.6 +/- 0.5 Ang) broad (FWHM = 1131 +\- 40 km/s) He II 1640 emission
lines in the nearby Universe and constitutes an important template for
interpreting observations of extreme He II emitters out to redshifts of z =
2-3. We use Cosmic Origins Spectrograph (COS) observations of A1 to show that
there is no significant contamination of the He II line with nebular emission
and that the line is redshifted by 121 +/-17 km/s relative to ISM lines. We
compare the COS G130M + G160M observations of A1 to recent binary BPASS and
single-star Charlot & Bruzual (C&B) simple stellar population (SSP) models with
Very Massive Stars (VMS) of up to 300 Msun. We suggest why BPASS models fail to
reproduce A1's He II emission. On the other hand, a C&B model with Z = 0.008,
age = 2.2 Myr, and VMS approaching the Eddington limit provides an excellent
fit to the He II emission and fits reasonably well C III 1175, N V 1238,1241,
and C IV 1548, 1551. We present O V 1371 line-profile predictions showing that
this line constitutes an important tracer of youth and VMS in galaxies.
Finally, we discuss the presence of VMS in CDFS131717, a highly star-forming
low-metallicity galaxy located at z = 3.071, which has a tentative detection of
O V absorption and strong broad He II emission. These features are rare and
hint to the presence of short-lived VMS in the galaxy. Our results show the
effect of the latest developments of stellar wind theory and the importance of
accounting for VMS in models.
