\(\int\limits_0^b\left[\int\limits_0^c \left(\int \limits_0^a (x^2 + y^2 + z^2)dx\right) dy\right]dz\)
\(= \int\limits_0^b \left(\int\limits_0^c \left(\frac {a^3}3 + ay^2 + az^2\right)dy\right)dz\)
\(= \int\limits_0^b \left(\frac {a^3c}3 + \frac {ac^3}3 + az^2c\right)dz\)
\(= \frac{a^3bc}3 + \frac{abc^3}3 + \frac{ab^3c}3\)
\(= \frac {abc}3(a^2 + b^2 + c^2)\)
