28 is just plain perfect.
Are you looking for something you'd implement with a programming language, or is this just a mathematical exercise?
If the former, and if you have a function that provides floating point cube roots, then something like this should do the trick:
y = round(cuberoot(x))
if (y*y*y == x) then x is a perfect cube
If the latter, determine the unique prime factorization of the absolute value of the number. If the exponents of all of the prime factors are multiples of 3, then the number is a cube. The number is also a cube if the number is zero or one.