Series of sum of cubes

[hearty quest]

Take the equivalence u found for each sum on the right

[latent cedar]

You can add and subtract the missing terms, such as:
\begin{align*} 1^3 + 3^3 + 5^3 &= 1^3 + 3^3 + 5^3 + \left(2^3 + 4^3 + 6^3\right) - \left(2^3 + 4^3 + 6^3\right) \ &= \left(1^3 + 2^3 + ... + 6^3\right) - \left(2^3 + 4^3 + 6^3\right) \end{align*}