Super star cluster (SSC) A1 (3.1 x10(5) M-circle dot) in NGC 3125 has one of the strongest ( EW = 4.6 +/- 0.5 A) broad ( F W H M = 1131 +/- 40 km s(-1)) He II lambda 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 similar to 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(-1) 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 M-circle dot. On the other hand, 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 lambda 1175, N V lambda lambda 1238, 1241, and C IV lambda lambda 1548, 1551. We present O V lambda 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.