Express $k$ as the sum of three square numbers

How do you express $k$ as the sum of three square numbers, if

$$m^2 + 3 = 2k$$
where both $m$ and $k$ are integers (both positive or negative if possible).

It is known that $m$ must be an odd integer, positive or negative, so that $k$ is an integer. It is also known that odd integers can be expressed as: $2n + 1$, where $n$ is an integer. Thus, how do you express $k$ as the sum of three square numbers?