Without actually calculating the cubes, find the value of each of the following :
i)\((-12)^3 + (5)^3 + (7))^3\)
ii)\((28)^3 + (-15)^3 + (-13)^3\)

We know that,
\(x^3 + y^3 + z^3 - 3xyz = (x + y + z)(x^2 + y^2 + z^2 - xy - yz - zx)\)

Also, if x + y + z = 0 then, \(x^3 + y^3 + z^3 = 3xyz\)


i) Here, -12 + 7 + 5 = 0

\(\therefore (-12)^3 + (5)^3 + (7))^3 \)
\( = 3(-12)(7)(5)\)
\(= -1260\)


ii)Here, 28 - 15 - 13 = 0
\(\therefore (28)^3 + (-15)^3 + (-13))^3 \)
\( = 3(-13)(28)(-15)\)
\(= 16380\)