Can You Solve This Math Problem?

Question

X^3 + Y^3 + Z^3 =  K    for all values of K from 1 to 100??
There is something special about K=42

So can you find the Values of X, Y, Z  when K = 42

? · Accepted Answer

No solutions for positive integers only, cubes adding to 42.
If negative integers allowed and we relax the 100 limit then ...

(80435758145817515)^3 + (-80538738812075974)^3 + (12602123297335631)^3 = 42.

Captain Matticus, LandPiratesInc · Answer

https://www.extremetech.com/computing/298112-life-the-universe-and-math-42-proven-to-be-the-sum-of-3-cubes

Jeffrey K · Answer

If X,Y,Z can be any real numbers, there are an infinite number of solutions. If they must be positive integers, there are no solutions for a K of 42.

? · Answer

Sure.  X = Y = Z = cube root of 14.

If you want integer solutions, you'd have to make one or two of the X, Y, Z negative, and I'm not sure that would produce a solution.