Final answer:
Chan will need a total of 343 cubes.
Step-by-step explanation:
Based on the given information, we can see that the bottom layer of the box consists of 7 cubes.
To find the total number of cubes needed to completely fill the box, we need to determine how many layers can be stacked on top of the bottom layer.
Let's assume the height of each cube is also 1 inch, so the height of the box is 7 inches (since there are 7 cubes in the bottom layer).
The total number of cubes needed is equal to the total volume of the box, which is the length multiplied by the width multiplied by the height. In this case, the length and width of the box are both 7 cubes, so the volume is 7 x 7 x 7 = 343 cubes.
Therefore, Chan will need a total of 343 cubes to completely fill the box.