A sealed rectangle or box measuring 8 x 6 x 18 contains 864 Sugar cubes each measuring one by one by one how many sugar cubes are touching the box

The arrangement of the 864 cubes would be 18 6 by 8 layers.

All 48 would be touching the bottom of the box on the bottom layer and all 48 would be touching the top of the box on the top layer.

The cubes along both lengths would be touching the sides of the box for the remaining 16 layers. That would be16 cubes per layer or 256 cubes after counting both sides.

The cubes along the width would be touching the ends of the box for those 16 layers. Those need to be eliminated from the count since the corner cubes were already counted as part of the ones touching the sides. 4 cubes have not been previously counted for each width of 6 cubes. Both ends of the 16 layers has 8 cubes per layer or 128 cubes.

Therefore, that is 256 (sides) + 128 (ends) + 48 (top) + 48 (bottom) and that totals to 480 cubes touching the box.