Find the sum of all 3-digit positive numbers \(N\) that satisfy the condition that the digit sum of \(N\) is 3 times the digit sum of \(N+3\).

**Details and assumptions**

The digit sum of a number is the sum of all its digits. For example, \(1123\) has a digit sum of \(1 + 1 + 2 + 3 = 7\).

The number \(12=012\) is a 2-digit number, not a 3-digit number.

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