I don't even have this cube!

This is a $\displaystyle 4\times 4\times 4$ Rubik's cube. It has $\displaystyle 401 196 841 564 901 869 874 093 974 498 574 336 000 000 000$ combinations! It has 9 trailing zeroes.

Find the number of trailing zeroes in the number of combinations of the $\displaystyle 25\times25\times25$ Rubik's cube.

Details :

• Do not disassemble the cube, it's expensive.
• Calculators are allowed.