Notice that for a=b=c=0, the relation `a^3=2b^3+3c^3` is a mathematical truth.

Since the number are integer, I'll propose you to consider the next possible solution: a=5, b=4 and c=-1.

`5^3 = 2*4^3 + 3*(-1)^3`

125 = 128 - 3

125 = 125

Of course, you can also use the possible solution a=-5,b=-4,c=1

`(-5)^3 = 2*(-4)^3 + 3*(1)^3`

-125 = -128 + 3

-125=-125

**ANSWER: The possible solutions of `a^3=2b^3+3c^3` are a=b=c=0;a=5, b=4 and c=-1; a=-5,b=-4,c=1.**

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