When n= 1

The above formula = 3 4-8-9 = 64.

find

Suppose that when n=k

3 (2k+2)-8k-9 is divisible by 64.

When n=k+ 1

Formula = 3 (2k+4)-8k- 17.

=9[3^(2k+2) -8k-9] +64k+64

Because 3 (2k+2)-8k-9 is divisible by 64.

∴ 9 [3 (2k+2)-8k-9]+64k+64 is divisible by 64.

When n=k+ 1, it holds.

According to the above, we know by mathematical induction.

2n+2 times of 3 -8n-9 can be divisible by 64.