Inorganic clathrate materials are of great fundamental interest and potential practical use for application as thermoelectric materials in freon-free refrigerators, waste-heat converters, direct solar thermal energy converters, and many others. Experimental studies of their electronic structure and bonding have been, however, strongly restricted by (i) the crystal size and (ii) essential difficulties linked with the clean surface preparation. Overcoming these handicaps, we present for the first time a comprehensive picture of the electronic band structure and the chemical bonding for the Sn24-x-δInxAs22-yI8 clathrates obtained by means of photoelectron spectroscopy and complementary quantum modeling.