For the record, I deleted this message. How it got to you so quickly I don't know since I deleted it almost as soon as I posted it. I realized that I had read the question wrong: there is nothing in the problem that says the number has to be the square and cube of the SAME integer as I supposed when I did the above analysis.
I believe the answer is 64 = 8^2 = 4^3, but I can only find that by trial and error. I presume someone will come along and show you how to do this.