A $3 \times 3$ square is filled with numbers: $a, b, c, d, e, f, g, h, i$ in the following way: Given that the square is magic (sums of the numbers in each row, column and each of two diagonals are the same), show that a) $2(a + c + g + i) = b + d + f + h + 4e$. (3) b) $2(a^3 + c^3 + g^3 + i^3) = b^3 + d^3 + f^3 + h^3 + 4e^3$. (3)