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If you fit them vertically you are bound to be stuck with the bottom 2 lines that can't have their bricks vertical (since you can't fit a 4 tall brick in a 2 tall space).

Therefore you can attempt to fit the top area with the use of vertical ones and at my best I could fit 36 bricks in a 6 x 4 x 6 in the x, y and z axis (y being the vertical axis).

You are left with the bottom 6 x 2 x 6 area in which you need to fit 17 bricks, put down horizontally since the bricks are too tall to fit in the area vertically.

For that you need a 6 x 1 x 6 design that can fit 8.5 bricks, and it is not possible to half the bricks so that one is ruled out, no matter the design you come up with.

The second design would be a design that encorporates all bricks laid down horizontally, without vertical bricks.

A 6 x 1 x 6 design (by the x y z axis) multiplied by 6 times, atop each other.

In the 1 tall area, you need to fit 53 bricks / 6 = 8.83 bricks per area, therefore this design wouldn't work either because you may not split the bricks.

I believe that you may not fit 53 bricks that are 1 x 1 x 4 into a 6 x 6 x 6 area.

I can provide designs I had mentioned, and I can highlight the mathematical part if needed.