To answer the question, we first calculate the area of the cube.
The area of a cube with side length s is given by
![A=6s^2](https://img.qammunity.org/2023/formulas/mathematics/college/eaqnlikw1x6jfxszwv8x2uk2fhnn220cwl.png)
Now in our case, s = 3.2 cm; therefore, the above gives
![A=6(3.2cm^{})^2](https://img.qammunity.org/2023/formulas/mathematics/college/fotmmxzrqngopfme4rec044obll18372fm.png)
![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.