Need better formula

I have to do Sum of sum of first N numbers , sum of squares of first N numbers and sum of cubes of first N numbers .

Is there any formula which can do summation of all three opration.
I have done this using Mathematical formula separately for these three and added them.
Here is my solution

Yes there is a formula but too complex

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May you tell the formula or send the link of that formula?

Faulhaberā€™s formula this is the formula

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http://oeis.org/A152457

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Faulhaberā€™s formula is new for me.
From the above link, I found the simple equation as
a(n) = n(n + 1)(3n^2 + 7n + 8)/12 which is able to find Sum of sum of first N numbers , sum of squares of first N numbers and sum of cubes of first N numbers.

Thank you!