Step 1: Recall concept.
Colour in transition metal ions arises due to $d$-$d$ electronic transitions in partially filled $d$ orbitals.
Step 2: Check ions.
- Cu$^+$ has configuration $[Ar] 3d^{10}$, fully filled $d$-orbitals $\Rightarrow$ no $d$-$d$ transitions, hence colourless.
- Cu$^{2+}$: $3d^9$, coloured.
- Ni$^{2+}$: $3d^8$, coloured.
- Fe$^{3+}$: $3d^5$, coloured.
Step 3: Conclude.
Only Cu$^+$ is colourless.
Final Answer:
\[
\boxed{Cu^+}
\]
% Quciktip