This study combines observations, large-eddy simulations (LES), and direct numerical simulations (DNS) in order to analyze entrainment and mixing in shallow cumulus clouds at all relevant spatial scales and, additionally, to verify the results by the multiple methods used. The observations are based on three flights of the CARRIBA campaign which are similar to the classical BOMEX case used for LES. Virtual flights in the LES data are used to validate the observational method of line measurements. It is shown that line measurements overrepresent the cloud core, and it is quantified how derived statistics depend on small perturbations of the flight track, which has to be taken in account for the interpretation of airborne observations. A linear relation between fluctuations of temperature and liquid water content has been found in both LES and observations in a good quantitative agreement. However, the constant of proportionality deviates from purely adiabatic estimates, which can be attributed to cloud edge mixing. The cloud edge is compared in detail in observations and LES, which agree qualitatively although the LES cloud edge is smoother due to the model's resolution. The resulting typical amplitudes of the turbulence fields from this comparison are compared with the large-scale forcing model which is used in a series of DNS which study the mixing below the meter scale, which show that LES does not resolve the intermittency of small-scale turbulence.