The electronic and nuclear spin degrees of freedom of donor impurities in silicon form ultra-coherent two-level systems that are potentially useful for applications in quantum information and are intrinsically compatible with industrial semiconductor processing. However, because of their smaller gyromagnetic ratios, nuclear spins are more difficult to manipulate than electron spins and are often considered too slow for quantum information processing. Moreover, although alternating current magnetic fields are the most natural choice to drive spin transitions and implement quantum gates, they are difficult to confine spatially to the level of a single donor, thus requiring alternative approaches. In recent years, schemes for all-electrical control of donor spin qubits have been proposed but no experimental demonstrations have been reported yet. Here, we demonstrate a scalable all-electric method for controlling neutral 31P and 75As donor nuclear spins in silicon. Using coplanar photonic bandgap resonators, we drive Rabi oscillations on nuclear spins exclusively using electric fields by employing the donor-bound electron as a quantum transducer, much in the spirit of recent works with single-molecule magnets. The electric field confinement leads to major advantages such as low power requirements, higher qubit densities and faster gate times. Additionally, this approach makes it possible to drive nuclear spin qubits either at their resonance frequency or at its first subharmonic, thus reducing device bandwidth requirements. Double quantum transitions can be driven as well, providing easy access to the full computational manifold of our system and making it convenient to implement nuclear spin-based qudits using 75As donors.