<p>I was a little unsure of this.
what is the maximum number of rectangular blocks measure 3inches by 2 inches by 1 inch that can be packed into a cube shaped box whose interior measures 6 einches on an edge? 3x2x1 is lxwxh? right then you just calculate how many fit at one level and divide by the height of the bigger cube to see how many layers?</p>
<p>If you are sure that the little blocks can be packed tightly to form the cube with no gaps inside and no bits sticking out, you can calculate the volume of the cube and divide by the volume of each block.</p>
<p>cube 6 inches on a side has volume 6^3 = 216 cubic inches.</p>
<p>block has volume 6 cubic inches.</p>
<p>216/6 = 36 blocks.</p>
<p>Your layer method also works, and it allows easy confirmation of dense packing.</p>
<p>6 blocks make a 6 by 6 square layer.
6 such layers make a 6 by 6 cube - 36 blocks.</p>
<p>L or T shaped blocks require more thought. Some larger blocks require more thought (for instance, a 4x4x4 block).</p>