Solution
Let b=6m Then a=9m and c=4m
$$a^3+b^3+c^3=8072$$
$$\left(9m\right)^3+\left(6m\right)^3+\left(4m\right)^3=8072$$
$$729m^3+216m^3+64m^3=8072$$
$$1009m^3=8072\ or\ m^3=8\ or\ m=2$$
Now a=9m or a=18
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