Answer:
Length: 1 cm.
Width: 1 cm.
Height: 1 cm.
Step-by-step explanation:
Hello,
In this case, since we are talking about a block as an example of rectangular prism, whose volume is computed via:

As such volume is 1 cm³ and each side measures 1 cm, we can assume that the length, width and height are all the same, 1 cm, in order to respect the 1-cm³ volume, thus:
Length: 1 cm.
Width: 1 cm.
Height: 1 cm.
We can proof this by solving:

Best regards.