Question 1030742
The perfect cubes are &#177;1, &#177;8, &#177;27, &#177;64, &#177;125, &#177;216, etc...

You want {{{3^6 = 729 <= q^2 <= 3^7 = 2187}}}, and incidentally only the perfect cube &#177;27 can satisfy this condition.

==> Q = {&#177;27}, hence the least member of Q is -27 and the greatest is 27.