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Mechanical cloaks are materials engineered to manipulate the elastic response around objects to make them indistinguishable from their homogeneous surroundings. Typically, methods based on material-parameter transformations are used to design optical, thermal, and electric cloaks. However, they are not applicable in designing mechanical cloaks, since continuum-mechanics equations are not form invariant under general coordinate transformations. As a result, existing design methods for mechanical cloaks have so far been limited to a narrow selection of voids with simple shapes. To address this challenge, we present a systematic, data-driven design approach to create mechanical cloaks composed of aperiodic metamaterials using a large precomputed unit cell database. Our method is flexible to allow the design of cloaks with various boundary conditions, multiple loadings, different shapes and numbers of voids, and different homogeneous surroundings. It enables a concurrent optimization of both topology and properties distribution of the cloak. Compared to conventional fixed-shape solutions, this results in an overall better cloaking performance and offers unparalleled versatility. Experimental measurements on additively manufactured structures further confirm the validity of the proposed approach. Our research illustrates the benefits of data-driven approaches in quickly responding to new design scenarios and resolving the computational challenge associated with multiscale designs of functional structures. It could be generalized to accommodate other applications that require heterogeneous property distribution, such as soft robots and implants design.