A box can be packed with a harmonic brick 
iff
the box has dimensions 
for some natural numbers 
, 
, 
(i.e., the box is a multiple of the brick).
de Bruijn's Theorem
See also
Box-Packing Theorem, Conway Puzzle, Klarner's TheoremExplore with Wolfram|Alpha
References
Honsberger, R. Mathematical Gems II. Washington, DC: Math. Assoc. Amer., pp. 69-72, 1976.Referenced on Wolfram|Alpha
de Bruijn's TheoremCite this as:
Weisstein, Eric W. "de Bruijn's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/deBruijnsTheorem.html