Question

any two cubic number that when added toghether gives anothere cubic number a^3+b^3=c^3. find a,b&c

Answer 1

No, your premise is not true.

2^3+3^2= a^3
8+27=
35, and 35 is not a cube of a natural number.

Answer 2

Fermat's Last Theorem states that there are no solutions to x^n + y^n = z^n for n = 3 or greater. Surprisingly, there are solutions to x^n + y^n = z^(n+1) or z^(n-1).

1--Divide through by z^n resulting in (x/z)^n + (y/z)^n = z.
2--Let (x/z) and (y/z) be any positive numbers other than 1.
3--Solve for z and then x and y.
4--Example: x^3 + y^3 = z^4
5--Let (x/z) = 2 and (y/z) = 5. Then 2^3 + 5^3 = 133 = z.
6--Then x = 2(133) = 266 and y = 5(133) = 665.
7--Checking: 266^3 + 665^3 = 18,821,096 + 294,079,625 = 312,900,721 = 133^4.
It works for any n and (n+1).