An object of dimensions L_o, W_o and H_o has a volume:

V_o = L_o W_o H_o

When the temperature changes the volume changes to:

V = L_o W_o H_o [1 + aDT]³

V = V_o [1 + 3aDT + 3(aDT)² + (aDT)³]

aDT is much less than 1, so (aDT)² and (aDT)³ are negligible. So:

V = V_o [1 + 3aDT]

V = V_o [1 + bDT]

where b, the coefficient of volume expansion, is three times larger than a the coefficient of linear expansion.