Evaluate \(21^3 + (-2)^3 + (-19)^3\)
2394
Let \(a = 21\), \(b = -2\) and \(c = -19\). Notice that \(a + b + c = 21 - 2 - 19 = 0\).
When \(a + b + c = 0\), the identity \(a^3 + b^3 + c^3 = 3abc\) holds.
So \(a^3 + b^3 + c^3 = 3 \times 21 \times (-2) \times (-19)\).
First, \((-2) \times (-19) = 38\), then \(21 \times 38 = 798\).
Therefore \(3 \times 798 = 2394\).
Hence, the value of the expression is 2394.
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