The cubic equation \(x^3 + 2x^2 + 3x + 3 = 0\) has roots \(\alpha, \beta, \gamma\).

(a) Find the value of \(\alpha^2 + \beta^2 + \gamma^2\).

(b) Show that \(\alpha^3 + \beta^3 + \gamma^3 = 1\).

(c) Use standard results from the list of formulae (MF19) to show that

\(\sum_{r=1}^{n} ((\alpha + r)^3 + (\beta + r)^3 + (\gamma + r)^3) = n + \frac{1}{4}n(n+1)(an^2 + bn + c),\)

where \(a, b, c\) are constants to be determined.