At the end of

https://encyclopediaofmath.org/index.php?title=Cubic_hypersurface#References

it is stated that the diagonal cubic hypersurface

$$ \sum_{i=0}^{2m+1} a_i x_i^3 = 0, m\ge 2 $$

(and presumably $a_i\not=0$) is rational. Is this true over the complex numbers, or any field of characteristic zero? Where can I find a reference of this result? Thanks!