We present the flux tables of the spectrophotometric standard stars (SPSS) used to calibrate in flux the Gaia DR2 and (E)DR3 data releases. The latest SPSS grid version contains 112 stars, whose flux tables agree to better than 1 per cent with the CALSPEC spectra of 11 flux standards for the calibration of the Hubble Space Telescope. The synthetic magnitudes computed on the SPSS spectra also agree to better than 1 per cent with the Landolt magnitudes of 37 stars in common. The typical spreads in both comparisons are of the order of 1 per cent. These uncertainties already meet the initial requirements for the Gaia SPSS project, but further improvements are expected in the next SPSS versions, that will be used to calibrate future Gaia releases. We complement the SPSS flux tables with literature spectra of 60 additional stars that did not pass all the criteria to be SPSS, the Passband Validation Library (PVL). The PVL contains stars of extreme spectral types, such as bright O and B stars and late M stars and brown dwarfs, and was useful to investigate systematic effects in the previous Gaia DR2 release and to minimize them in the EDR3 one. The PVL literature spectra are recalibrated as accurately as possible on to the SPSS reference scale, so that the two sets together can be used in a variety of validation and comparison studies.