# Further Maths - Sums of Cubes

> Source: https://ollybritton.com/notes/a-level/further-maths/topics/sums-of-cubes/ · Updated: 2020-09-16 · Tags: further-maths, series, school

##### What is the formula for the sum of the cubes of the first $n$ natural numbers??
$$
\sum^{n}_{r=1} r^3 = \frac{1}{4}n^2(n+1)^2
$$

##### How could you rewrite $\sum^{n}_{r=1} r^3$??
$$
\frac{1}{4}n^2(n+1)^2
$$

##### What's another way of expressing $\frac{1}{4}n^2(n+1)^2$??
$$
\sum^{n}_{r=1} r^3
$$

##### How could you rewrite $\sum^{n}_{r=1} 4r^2$??
$$
n^2(n+1)^2
$$

##### What's an easy way for remembering the sum of cubes formula??
It's the sum of the natural numbers formula squared.

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