A modulation format recognition (MFR) scheme based on multi-core fiber (MCF) is proposed for the next generation of elastic optical networks (EONs). In this scheme, multiple Stokes sectional planes images are used as signal features which are typed into a transfer learning (TL) assisted convolutional neural network (CNN) to realize MFR. Compared with the traditional Jones matrix, the Stokes space mapping method is insensitive to polarization mixing, carrier frequency skew and phase offset, therefore, it has better feature representation ability. TL is introduced to transfer the model used in standard single-mode fiber (SSMF) to MCF transmission, reducing the required training data and complexity. In addition, multiple Stokes sectional planes images are input simultaneously, which improves the accuracy of the neural network. Experimental verifications were performed for a polarization division multiplexing (PDM)-EONs system at a symbol rate of 12.5GBaud by 5 km MCF. Nine modulation formats, including three standard modulation formats (BPSK, QPSK, 8PSK), three uniformly shaped (US) modulation formats (US-8QAM, US-16QAM, US-32QAM) and three probabilistically shaped (PS) modulation formats (PS-8QAM, PS-16QAM, PS-32QAM), were recognized by our scheme. The experimental results show that the scheme achieves high recognition accuracy even at low optical signal-to-noise ratio (OSNR). Moreover, the required number of training samples is less 40% compared to the traditional CNN. The proposed scheme has a high tolerance to the crosstalk damage of MCF itself and can realize the short training time of large-capacity space division multiplexing (SDM)-EONs. Our findings have the potential to be used in the next generation of a SDM fiber transmission system.