KöMaL 2012 C1125

A table of three columns is filled in with numbers as follows: The number $2^n$, without its digit in the units' place, is entered in the field at the intersection of the first column and the $n$th row. The digit that was cancelled in the first column is entered in the field in the $n$th row of the second column. Finally, the entry in the third column and the $n$th row will be the product of the first two entries of the same row. Prove that the numbers in the third column are all divisible by six.