Given the polynomial \( P(x) = x^3 - 3x^2 + 3x - 1 \), evaluate \( P(4) \). Then, consider the combinatorial sum of evaluating \( P \) at all integers from 1 to 5 and find the sum of these values. Finally, if \( P(x) \) is factored into a product of linear factors, find the sum of the roots of \( P(x) \). Let's think step by step and output the final answer within \boxed{}.
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