The formula for the volume of a regular solid is length x width x height. Because for a cube all these dimensions are the same, you need only measure one of these and multiply it by itself, and then by itself again.
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A ruler. Measure one of the sides, and take that measurement times itself three times, and you'll have the volume.
The answer depends on the size of the cube: it could be a micrometre, vernier callipers, a ruler, a tape measure.
All you need is a graduated ruler to measure the length of one edge. From there one calculates the volume. For a cube, which has edges of equal length, you can find the the volume by cubing the length of an edge. Vcube = e3
Yarn , because that can rap around the cube OR you could use stringy ruler type thing
Scales to measure its mass and a ruler to measure the length of the cube's side.