IZhO 2008 Problem 2

A polynomial $P(x)$ with integer coefficients is called good,if it can be represented as a sum of cubes of several polynomials (in variable $x$ ) with integer coefficients.For example,the polynomials $x^3 - 1$ and $9x^3 - 3x^2 + 3x + 7 = (x - 1)^3 + (2x)^3 + 2^3$ are good. a)Is the polynomial $P(x) = 3x + 3x^7$ good? b)Is the polynomial $P(x) = 3x + 3x^7 + 3x^{2008}$ good? Justify your answers.