What a the algorithm to find wheather a number is prefect cube or not?

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.

You can also use logarithms. If x is the number, then find the logarithm of x and divide it by 3. Then take the antilog of that number. If the resulting number is an integer it is a perfect cube.

Effectively I'm doing the same thing markr is recommending--it's just this is a calculator algorithm.

Rap