An algebra problem by Abhay Kumar

Algebra Level 4

Let \(a\) be the arithmetic mean of \(b\) and \(c.\) Furthermore, let \(g_1\) and \(g_2\) be two numbers such that \(b, g_1, g_2, c\) forms a geometric sequence.

What is the value of \(g_1^3 + g_2^3\)?

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