Given,
2x3 + 54y3 - 4x - 12y
= 2(x3 + 27y3) - 4(x + 3y)
= 2[(x)3 + (3y)3] - 4(x + 3y)
= 2(x + 3y)(x2 - 3xy + 9y2) - 4(x + 3y) [∵ a3 + b3 = (a + b)(a2 - ab + b2)]
= 2(x + 3y)(x2 - 3xy + 9y2 - 2).
Hence, 2x3 + 54y3 - 4x - 12y = 2(x + 3y)(x2 - 3xy + 9y2 - 2).