The spectral energy distributions (SEDs) of a sample of 142 LMC and 77 SMC fundamental mode classical Cepheids (CCs) were constructed using photometric data in the literature. The data was whenever possible representative of mean light, or averaged over the light curve. The sample was build from stars that have a metallicity determination from high-resolution spectroscopy, have been used in Baade-Wesselink type of analysis, have a radial velocity curve published in Gaia DR3, have Walraven photometry, or have their light- and radial-velocity curves modelled by pulsation codes. The SEDs were fitted with stellar photosphere models to derive the best-fitting luminosity and effective temperature. Distance and reddening were taken from the literature. The stars were plotted in a Hertzsprung-Russell diagram (HRD) and compared to evolutionary tracks for CCs and to theoretical instability strips. For the large majority of stars, the position in the HRD is consistent with the instability strip. Period-luminosity (PL) and period-radius relations are derived and compared to these relations in the MW. For a fixed slope, the zero point of the bolometric PL relation does not depend on metallicity, contrary to recent findings of a significant metallicity term when considering the PL relation in different photometric bands. The mass-luminosity (ML) relation is derived and it points to an over luminosity of about +0.3dex with respect to a canonical ML relation. The most intriguing result concerns the flux-weighted gravity (FWG, a quantity derived from gravity and effective temperature) and its relation to period and luminosity. Both relations agree with theory, with the results for the MW, and with the independent estimates from the six known LMC eclipsing binaries that contain CCs. However, the FWG as determined from dedicated high-resolution spectroscopy for the sample is too low by about 0.8dex in 90% of the cases. Recent work on time-series data on 20 CCs in the MW was analysed to find a similar (but less extreme) offset in gravity and the FWG. Importantly, other time-series data on the same 20 CCs are in full agreement with the FWG-period relation however. The observed time-series of spectroscopic data and from a two-dimensional hydrodynamical cepheid model was used to investigate the so-called effective gravity, that is, the gravity corrected for a dynamical term related to the time derivative of the radial velocity. There is a reasonable good correspondence between the predicted effective gravity and the observed gravity as a function of pulsation phase, which potentially would allow for an independent estimate of the projection factor, but the dynamical term is too small to explain the overall difference between the observed (flux weighted) gravity, and the (flux weighted) gravity derived from the SED modelling and stellar mass estimates.