Explanation:
well, a volume is the amount of space inside an object.
and a side length is just the length of a side of an object.
you see, we can measure the length of a wall of a room, and we can determine if a special piece of furniture could fit there.
that is measured in a one-dimensional metric (only length) and would be meters or feet or yards or similar.
but even if the answer is yes, we don't know, if we actually want to do that, because we have no clue how that would fit with the rest we want to put into the room.
so, we measure now the the lengths of all walls and determine the area of the room.
now we have a better understanding how much furniture we can get into the room, and if there is enough space to walk in between and so on.
that is measured in a 2-dimensional metric (length×width) and would be meters², feet², yards², or similar.
you see, the difference is that we cannot express an area by pieces of strings or sticks that we use for length.
now we need to use standard pieces of area like a standard square to express how many of these standard areas fit into the floor of that room.
1 m² is e.g. the standard square of 1 meter side length.
an answer like 15 ft² tells is that the area is so large, that we can fit 15 steadfast squares of 1ft side lengths into it.
a rectangle of 3 ft × 5 ft does exactly that. it is like putting tiles in the floor.
we start with the first row of 5 standard tiles, then the second row of 5, and then the 3rd row of 5. and then we are out of space. 15 ft² squares.
and now we also want to know, how much air there is in the room to e.g. find the right dimension of an air conditioning system for that room (and maybe some other rooms too).
so, we need to know the space, the volume inside the room to know how much air there is in the room.
we cannot get this from a length of a wall, and not even from the area of the floor.
no, we need to include the height of the room as the third dimension.
so, this is measured in a 3-dimensional metric (length×width×height) like meters³, feet³, yards³ or similar. in this case we have also some special metrics for gasses or liquids like liter or gallons, and they all have their criss-cross conversion rules and rates.
in the 3- dimension case we do not use a standard length or a standard square. no, we use standard cubes.
1 m³ is a standard cube with 1 m side length.
an answer like 135 ft³ treks me that that is a prism or block, where I can put in 135 standard cubes with 1 ft side length.
if it is or previous rectangle of 3 ft ×5 ft, then it's height is 9 ft, and so 3×5×9 = 135 ft³.
and we could start with a first row of 5 cubes, then a 2nd and a 3rd row, and then we create a second layer on top of that first one, again with a first row of 5 cubes, then a 2nd and a 3rd. and then a 3rd layer and a 4th and so on up to the 9th layer of 3 rows of cubes.
that is the concept here.
if you tell me 135 ft, I think you only give me a length.
if you tell me 135 ft², I think you only want to give me an area.
but if you tell me 135 ft³, then I know you are really talking about the space inside the block or room.
that is why this is done that way, and I hope you understand now the difference.
the European metric system has the advantage that all metrics about length, area, volume, and even weight are completely connected by the base of 10.
1 liter of water fits exactly into a cube with the side length of 10 cm (= 0.1 meter). so, in 1 m³ we have 10×10×10 such cubes, that means it contains 1000 liters.
and 1 liter of water weighs exactly 1 kilogram (1000 grams).
and so on.
the American system has special conversion rules for most of their counterparts, but most with their own constants, and it is very difficult to understand how to get from gallons to yards³ and to pounds.