if m is an integer is \(m^3\cdot 3^{k+3}-m^2\cdot 3^{2k+3}+m\cdot 3^{k+2}-1\)an integer??
Assuming that k is also a positive integer and that the backslant does not mean divide, I don't see anything in the expression that would introduce a fraction. Of course, I don't know what the "cdot" means so I ignored it.
I think what s/he meant was
If m is an integer is \(m^3\cdot 3^{k+3}-m^2\cdot 3^{2k+3}+m\cdot 3^{k+2}-1\) an integer?