First show that the statement is true for n = 2. Which infact is.

Now assume

is true.

Consider

Which is same as

which on simplification gives

Now by assumption is divisible by 64 and for k > 2 64k is divisible by 64.

So statement is true for k + 1

Hence proved.

P.S I am new to this forum and am learning how to type mathematical expressions. So ignore any typing mistake.