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## Main Question or Discussion Point

Hi, I would like some help in proving the following identity:

[tex]\sum_{x=0}^{n}x^3 = 6\binom{n+1}{4} + 6\binom{n+1}{3} + \binom{n+1}{2}[/tex]

I tried doing it by induction but that did not go well (perhaps I missed something). Someone told me to use the fact that [tex]\binom{x}{0}, \binom{x}{1},...,\binom{x}{k}[/tex] span the space of polynomials of degree k or less [tex]\mathbb{R}_k[x][/tex], but I didn't really see how to use that. Any help would be welcome, but I'd rather it would not be the whole solution but rather hints.

Thanks a lot and have a good day.

[tex]\sum_{x=0}^{n}x^3 = 6\binom{n+1}{4} + 6\binom{n+1}{3} + \binom{n+1}{2}[/tex]

I tried doing it by induction but that did not go well (perhaps I missed something). Someone told me to use the fact that [tex]\binom{x}{0}, \binom{x}{1},...,\binom{x}{k}[/tex] span the space of polynomials of degree k or less [tex]\mathbb{R}_k[x][/tex], but I didn't really see how to use that. Any help would be welcome, but I'd rather it would not be the whole solution but rather hints.

Thanks a lot and have a good day.