In any complete graph Kn, number of cycles possible of m vertices are:
nCm (m-1)!/2
Now, for maximum number of cycles, we should count all cycles possible and we know to make cycle we need minimum 3 vertices,
Maximum = nC3 + nC4 (3!/2) + nC5 (4!/2) +....+ nCn (n-1)!/2
Is my calculation is right or wrong let me know!