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Given the positive integers a≤b≤c≤100a \le b \le c \le 100 a≤b≤c≤100 satisfy the system of equations below.
{a+b=ca4+b2=c2a3=b+c \begin{cases} {a+b=c} \\ {a^4+b^2=c^2} \\ {a^3=b+c} \\ \end{cases} ⎩⎪⎨⎪⎧a+b=ca4+b2=c2a3=b+c
Find the sum of all possible values of a+b+ca+b+ca+b+c.
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