The feasibility of transmitting discrete-variable quantum key distribution channels with carrier-grade classical optical channels over multicore fibers is experimentally explored in terms of achievable quantum bit error rates, secret key rates as well as classical signal bit error rates. A coexistence transmission record of 11.2 Tb/s is achieved for the classical channels simultaneously with a DV-QKD channel over a 1 km-long 7-core multicore fiber. Coexistence over the same multicore fiber core is identified as a dominant factor for the performance of the quantum channel requiring optical bandpass filtering of 17 nm for the quantum channel to avoid the effect of Raman noise. Also, counter-propagation of classical channels and quantum channels probe more tolerance to noise proliferation than co-propagation. In addition, the performance of the quantum channel is maintained when more than three cores are used for the classical channels. Furthermore, by adding a second DV-QKD channel in the multicore fiber, the simultaneous transmission of classical channels as well as the generation of quantum-secured keys of two QKD channels is achieved with an operational range of 10 dB of launched power into the MCF.