A 6x10x14 rectangular cuboid is made by stacking together 6*10*14 = 840 unit cubes. An elliptic cone having minor axis = 6 units; major axis = 10 units, and height = 14 units is cut out of the cuboid by means of an infinitely thin laser-like cutting tool.

How many unit cubes will stay undamaged inside the elliptic cone?