Inches vs Inches^3 Peace to all.  After gathering and calculating the measurements by volume (of a box), will the results be in regular inches or will they be in inches^3?
For example, if the dimensions of the item are as follows:  L = 4.13in, W = 5.50in, H = 7.50in, will the result of the volume be 170.36in or 170.36in^3
When is inches^3 appropriate compared to inches?....Does the same rule apply to all measurements in this scenario (such as CM, MM, etc)?
 A: You can sort of treat the units as quantities. The volume is $4.13\text{ in}\times 5.50\text{ in}\times 7.50\text{ in}=(4.13\times 5.50\times 7.50)(\text{in})^3$. Hence, the unit of volume is $\text{inches}^3$. In general, you can apply this strategy of treating units as a variable/quantity in order to find the units for another property/measurement calculated from a formula. It can also be helpful when figuring out unit conversions.
A: A volume is always measured in length3. In your case, length is inches.
Outside of physics, people may not be quite so careful, or knowledgable. If you buy a chainsaw, you might be told it has a 1.6" engine. In context, it obviously means cubic inches. You're smart enough to figure that out. The chainsaw salesman may neither appreciate nor understand a correction.
A: Indeed the measurement of the volume of the box will be in inches cubed, i.e. $\text{in}^3$.
The same goes for other units: If the side length of the box is in centimeters ($\text{cm}$), then the volume of the box will have units $\text{cm}^3$.
A: If $X$ is the number of cubic units $\space (u)\space$ it is always appropriate to write
$ X\space  u^3\space$ as opposed to $X^3 u.\quad$
The distinction is important where, for example, $X>1\implies  X^2 mi >Xmi^2.\quad$  Oddly enough, casual language portrays it the other way: "$X\space$ square miles is less than $X\space$ miles squared," where the  latter refers to a square that is $X$ miles on a side.
In your example each $1D$  measurement is expressed as a unit to the first power but the final expression shows the unit cubed.
$$4,13\space in\space \times\space 5.5\space in\space \times\space  7.5\space in
= 170.3625\space in^3$$
