# Further Maths - Sums of Cubes

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.