A steady current flow in a long wire.it is bent into a circular loop of one turn and magnetic field at centre is B.if same wire is bent into a circular loop of n turns magnetic field at the centre of the coil is

Here length of the wire is considered fixed. So the radius of the small turns r=R/N; where R the radius of the big circular loop.

then B=Mu_0* I/(2*pi*R)

and for the later case mag. field =Mu_0*I/(2*pi*(R/N))

=BN.

Edit1: But the current also increases N times so the ans is BN^2.