A weighted multidimensional Cochran-Lee inequality is characterized in the frame of Hardy-type inequalities with parameters 0<p≤q<∞. Moreover, for the case p=q and power weights, even the sharp constant is derived, thus generalizing the original Cochran-Lee inequality to a multidimensional setting. As an application, new inequalities are pointed out. Finally, some related Hardy-type inequalities on homogeneous groups are presented.