In the equation (w^3 + x^3 + y^3 = z^3) , w^3, x^3, y^3, and z^3 are distinct consecutive positive perfect cubes listed in ascending order. What is the smallest possible value of z?
The smallest possible value of z=6, so that:
w^3+x^3+y^3 =z^3
3^3 + 4^3 + 5^3 = 6^3
27 + 64 + 125 = 216
+237 
