# Is it possible to build a $8×8×9$ block using $32$ bricks of dimensions $2×3×3$?

Is it possible to build a $$8×8×9$$ block using $$32$$ bricks of dimensions $$2×3×3$$?

I tried to show that $$8×8×9$$ block can't contain $$32$$ blocks of dimensions $$2×3×3$$ . For that I tried to colour $$1×1×1$$ cubes.

(It would give me something like dominoes on chessboard where you can't use $$1$$ cell so blacks are more than whites , but domino covers the same number of blacks and whites)

I thought that I have to colour them in $$18$$ colours , but that's too much , and impossible to visualise in three-dimensional space.

The large block will have an $$8\times 8$$ face. It must break down into $$2\times3$$ and $$3\times3$$ faces. So each small face has area divisible by $$3$$, yet the total area of that face, $$64$$, is not divisible by $$3$$.