MatheMania

If:

    a +  4 b +  9 c + 16 d + 25 e + 36 f + 49 g = 1

 4 a +  9 b + 16 c+ 25 d + 36 e + 49 f + 64 g = 12

 9 a + 16 b+ 25 c + 36 d + 49 e + 64 f + 81 g = 123

Find the value of:

16 a+ 25 b + 36 c + 49 d + 64 e + 81 f + 100g