As we know the Answer to the Ultimate Question of Life, The Universe, and Everything is 42.

In 2020 the University of Bristol and MIT found a solution to 42 that fits the sums of three cubes

For k = 42,
x = -80538738812075974
y = 80435758145817515
z = 12602123297335631

Proof:
x^3 = -522413599036979150280966144853653247149764362110424
y^3 = 520412211582497361738652718463552780369306583065875
z^3 = 2001387454481788542313426390100466780457779044591

x^3 + y^3 + z^3 = 42