An experiment on the measurements of the Cherenkov light yield of inclined cosmic ray muon bundles in water is being conducted at the Experimental complex NEVOD (MEPhI). The total number of Cherenkov photons is nearly proportional to the muon energy deposit (including secondary particles and cascades from them) within the detector volume. Since in the muon energy range above a hundred GeV the energy loss is linearly related to the energy of muons (dE/dX ~ a + bE), the average energy loss of the bundles carries the information about the mean muon energy in such events. The complex includes the Cherenkov water calorimeter NEVOD with a volume of 2000 cub. m and the coordinate-tracking detector DECOR (total area of 70 sq. m). The DECOR data are used to determine the local muon densities in the bundle events and their arrival directions, while the energy deposits are evaluated from the Cherenkov calorimeter response. The detection of the bundles in a wide range of muon multiplicities and zenith angles gives the opportunity to explore the energy range of primary cosmic ray particles from about 10 PeV to 1000 PeV in frames of a single experiment. Experimental results on the dependence of the muon bundle energy deposit on the zenith angle and the local muon density will be presented and compared with expectations based on simulations of the EAS muon component by means of the CORSIKA code and of the response of the Cherenkov calorimeter with the Geant4 toolkit.