Who is asking: Student
The question is:
I have no clue how to do this. Please help me figure it out. Thank You.
A cube is three-dimensional so the cubes you mention are 3x3x3, 4x4x4, 55x5 and 6x6x6. Now I can see where the numbers come from.
A 3x3x3 cube is made from 27 cubes and a 2x2x2 cube is made from 8 cubes. 27 - 8 = 19 and hence the numbers in the first row.
A 4x4x4 cube is made from 64 cubes and a 3x3x3 cube is made from 27 cubes. 64 - 27 = 37 and hence the numbers in the second row.
In each row the ARITHMETIC pattern is
If you have 27 identical blocks and you start to construct a 3x3x3 cube you immediately see that there is 1 block that is hidden.
If you have 64 identical blocks and you start to construct a 4x4x4 cube you immediately see that there are 8 block that is hidden.
If you have n3 identical blocks and you construct an nxnxn cube there are (n-2)3 block that is hidden.
Paul and Penny