We present VLT/MUSE observations of NGC 2070, the dominant ionizing nebula of 30 Doradus in the LMC, plus HST/STIS spectroscopy of its central star cluster R136. Integral Field Spectroscopy (MUSE) and pseudo IFS (STIS) together provides a complete census of all massive stars within the central 30×30 parsec2 of the Tarantula. We discuss the integrated far-UV spectrum of R136, of particular interest for UV studies of young extragalactic star clusters. Strong He iiλ1640 emission at very early ages (1–2 Myr) from very massive stars cannot be reproduced by current population synthesis models, even those incorporating binary evolution and very massive stars. A nebular analysis of the integrated MUSE dataset implies an age of ~4.5 Myr for NGC 2070. Wolf-Rayet features provide alternative age diagnostics, with the primary contribution to the integrated Wolf-Rayet bumps arising from R140 rather than the more numerous H-rich WN stars in R136. Caution should be used when interpreting spatially extended observations of extragalactic star-forming regions.