GAUSS7 2002 Problem 16

In the following equations, the letters a,b and c represent different numbers.

\begin{aligned} & 1^3=1 \\ & a^3=1+7 \\ & 3^3=1+7+b \\ & 4^3=1+7+c \end{aligned}

The numerical value of a+b+c is

Answer Choices
A. 58
B. 110
C. 75
D. 77
E. 79