Recently, a framework was given to construct low ML decoding complexity Space-Time Block Codes (STBCs) via codes over the finite field double-struck F4. In this paper, we construct new full-diversity STBCs with cubic shaping property and low ML decoding complexity via codes over double-struck F4 for number of transmit antennas N=2m, m > 1, and rates R > 1 complex symbols per channel use. The new codes have the least ML decoding complexity among all known codes for a large set of (N,R) pairs. The new full-rate codes of this paper (R=N) are not only information-lossless and fully diverse but also have the least known ML decoding complexity in the literature. For N ≥ 4, the new full-rate codes are the first instances of full-diversity, information-lossless STBCs with low ML decoding complexity. We also give a sufficient condition for STBCs obtainable from codes over double-struck F4 to have cubic shaping property, and a sufficient condition for any design to give rise to a full-diversity STBC when the symbols are encoded using rotated square QAM constellations. © 2011 IEEE.