It's known that any Gaussian integer can be represented as the sum of three squared Gaussian integers. (See my other problem.)
Let $A$ and $n * A$ be sets of complex numbers, where $n$ is some positive integer. Then $x \in n*A$ if and only if $x$ is the distinct sum of $n$ elements of $A$.
Define $G=\{z\mid z=(a+bi)^3, a+bi \in \mathbb{Z}[i]\}$ and $K=\mathbb Z[i]$.
What is the smallest integer $n$ such that $K=n*G$ ?
Waring's problem states that every number is the sum of at most 9 cubes, hence $n\leq 18: \sum x_i^3+i\sum y_i^3=\sum x_i^3+\sum (-y_ii)^3$.