Explanation: To solve this question we will work with the conversion from cm to mm as follows
[tex]\begin{gathered} 1cm=10mm \\ 1mm=0.1cm \end{gathered}[/tex]Step 1: First let's convert our length from cm to mm to be able to visualize our problem better as follows
[tex]\begin{gathered} once\text{ 1cm=10cm} \\ then\text{ 0.178cm=1.78mm} \end{gathered}[/tex]Step 2: Now once the cube has all the sides equal we can use the cube's volume formula to calculate as follows
[tex]V_{cube}=side^3=1.78^3=5.639752mm^3\cong5.64mm^3[/tex]Step 3: Now all we have to do is to transform back to cm if we want to get the volume in centimetres
[tex]\begin{gathered} once\text{ 1mm=0.1cm} \\ then\text{ 5.64mm=0.564cm}^3 \end{gathered}[/tex]Final answer: So the final answer is
[tex]\cong0.564cm^3[/tex].
