A problem by Jason Sebastian

Level pending

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. There are \(N\) \(terryfic\) numbers between 1 and 2014 inclusively.

What are the last three digits of \(N + 437\)?

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