Without actually calculating the cubes, find the value of: [cube of (-12)] + [cube of (7)] + [cube of (5)]?

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=3*-12*7*5 =-1260
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The given expression is in the form of (a+b+c)^3. As on adding a,b,c we are getting 0, we can apply the formula: If a+b+c = 0 then, (a+b+c)^3 = 3 abc; On applying the above formula, we get (-12) ^3+(7)^3+(5)^3 = 3(-12)(7)(5) = - 1260.
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