When materials are exposed to X-ray pulses with sufficiently high intensity, various nonlinear effects can occur. The most fundamental one consists of stimulated electronic decays after resonant absorption of X-rays. Such stimulated decays enhance the number of emitted photons and the emission direction is confined to that of the stimulating incident photons which clone themselves in the process. Here we report the observation of stimulated resonant elastic (REXS) and inelastic (RIXS) X-ray scattering near the cobalt L3 edge in solid Co/Pd multilayer samples. We observe an enhancement of order 106 of the stimulated over the conventional spontaneous RIXS signal into the small acceptance angle of the RIXS spectrometer. We also find that in solids both stimulated REXS and RIXS spectra contain contributions from inelastic electron scattering processes, even for ultrashort 5 fs pulses. Our results reveal the potential and caveats of the development of stimulated RIXS in condensed matter.