Open-loop and feedback potential differential games for multi-agent systems are considered in this pa-per. Constructive sufficient conditions under which a linear quadratic differential game constitutes a potential differential game are provided. The conditions enable the construction of associated optimal control problems that yield (at signifi-cantly reduced computational complexity) solutions (in terms of open-loop and feedback Nash equilibrium strategies) of the original differential game. The results are demonstrated on a practically-motivated example that concerns spacecraft formation control.