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Cubing multiplies a number by itself twice more. Unlike squaring, cubing preserves sign, so the cube of a negative number is negative.
Cube
x³ = x × x × x
Difference of cubes
a³ − b³ = (a − b)(a² + ab + b²)
343 and 512, differing by 169.
Three negative factors multiply to a negative, whereas the even count in squaring cancels the sign.