Here we have three solid cubes and three cubes that have holes.
They're just the first three in a series that could go on and on.
I was wondering about the number of cubes used in each ...
Then I thought about the difference between those numbers.
So, for example, I found that the first cube, $3$ by $3$ by $3$, used $27$ cubes.
The same cube with holes used $20$ cubes, a difference of $7$.
You can call these types of cubes what you like but I called them "Solid" and "Frame".
How about exploring the numbers for the next few Solid and Frame cubes?
Do you notice any patterns?
Can you explain any of the patterns?