If α, β and γ are coefficient of linear, area and volume expansion respectively, then

$$\begin{gathered} V + ∆V = {(L + ∆L)}^3 = {(L + \alpha L∆T)}^3 = L^3+ (1 + 3\alpha ∆T + 3\alpha 2∆T^2+{\alpha }^3∆T^3 ) \\ \Rightarrow {\alpha }^2 and {\alpha }^3 terms are neglected. \\ \therefore V (1 + \gamma ∆T) = V (1 + 3\alpha ∆T) \\ 1 + \gamma ∆T = 1 + 3\alpha ∆T \\ \therefore \gamma = 3\alpha \end{gathered}$$