Let a number be *\(terryfic\)* if it can be expressed as \(a^3+b^3+c^3\), where \(a\), \(b\) and \(c\) are distinct positive integers.

What are the last three digits of the **\(sum\)** of all *\(terryfic\)* numbers between \(1\) and \(2014\) inclusively?

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