A polycube in dimension $d$ is a finite union of unit $d$-cubes whose vertices are on knots of the lattice $\mathbb{Z}^d$. We show that, for each family of polycubes $E$, there exists a finite set $F$ of bricks (parallelepiped rectangles) such that the bricks which can be tiled by $E$ are exactly the bricks which can be tiled by $F$. Consequently, if we know the set $F$, then we have an algorithm to decide in polynomial time if a brick is tilable or not by the tiles of $E$.
Garvie, Marcus R.; Burkardt, John, 2022, A Parallelizable Integer Linear Programming Approach For Tiling Finite Regions Of The Plane With Polyominoes, Algorithms, 15, 5, pp. 164, 10.3390/a15050164.
Karademir, Serdar; Prokopyev, Oleg; Mailloux, Robert J., 2015, Irregular Polyomino Tiling Via Integer Programming With Application In Phased Array Antenna Design, Journal Of Global Optimization, 65, 2, pp. 137-173, 10.1007/s10898-015-0354-8.