To answer the question, we first calculate the area of the cube.
The area of a cube with side length s is given by

Now in our case, s = 3.2 cm; therefore, the above gives

![A=61.44\operatorname{cm}^2\text{.}]()
Now, we are told that all sides have been painted except for one; therefore, we subtract the area of one side from above to get:
![61.44\operatorname{cm}-3.2\operatorname{cm}^2]()
![=51.2\operatorname{cm}^2]()
Hence, 51.2 square units will be painted.