Several letters appear only three times in the set of letters. These three must be three words crossing at a single instance of this letter in one of the word cubes. These can be used to reconstruct the cubes (shown below in a likely order of reconstruction):
JAM PGA LON OBI ROC EWE TAX OPT EEC ZOE ALS GDP IDS VIE ERA PDQ ADE LED CPU PEZ ARI HUN USA DEM ENO TSP SAP EGG TNT CUE TAP ITO AFT AMA SHY POE TOM ALI DEA MCI RAN ILK CTR CSN SKA
The central letters can be rearranged to spell the answer, IOTAS.