It would take 8 blocks with a side length of 1/6 inch to fill the cube.
it would take 27 blocks with a side length of 1/9 inch to fill the cube.
To solve this problem
We need to consider the ratio of their volumes.
Blocks with side length 1/6 inch:
The ratio of the side lengths is

The ratio of the volumes is

So, it would take 8 blocks with a side length of 1/6 inch to fill the cube.
Blocks with side length 1/9 inch:
- The ratio of the side lengths is

- The ratio of the volumes is

Therefore, it would take 27 blocks with a side length of 1/9 inch to fill the cube.