The system is not time invariant
Let time delay = t
then
Xk[n]=δ[n-k] -> time delay -> system
equals to X(k+t)[n]=δ[n-(k+t)]->system
equals to X(k+t)[n]=δ[n-k-t]->system
equals to Y(k+t)[n]=$ (k+t+1)^2 $ δ[n-(k+t+1)]
while
Xk[n]=δ[n-k] -> system -> time delay
equals to Yk[n]=$ (k+1)^2 $ δ[n-(k+1)]->time delay
