DE-MO 1998 Problem 3

For each nonnegative integer $k$ find all nonnegative integers $x,y,z$ such that $x^2 +y^2 +z^2 = 8^k$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.