Nature uses a combination of non-covalent interactions to create a hierarchy of complex systems from simple building blocks. One example is the selective association of the hydrophobic side chains that are a strong determinant of protein organization. Here, we report a parallel mode of assembly in DNA nanotechnology. Dendritic alkyl-DNA conjugates are hybridized to the edges of a DNA cube. When four amphiphiles are on one face, the hydrophobic residues of two neighbouring cubes engage in an intermolecular 'handshake', resulting in a dimer. When there are eight amphiphiles (four on the top and bottom cube faces, respectively), they engage in an intramolecular 'handshake' inside the cube. This forms the first example of a monodisperse micelle within a DNA nanostructure that encapsulates small molecules and releases them by DNA recognition. Creating a three-dimensional pattern of hydrophobic patches, like side chains in proteins, can result in specific, directed association of hydrophobic domains with orthogonal interactions to DNA base-pairing.