Intensive research into functional oxides has been triggered by the quest for a solid-state universal memory with high-storage density, non-volatility, high read/write speed, and random access. The ferroelectric random-access memory (FeRAM), in which the information is stored in the spontaneous ferroelectric polarization of the material, offers great promise as nonvolatile and multistate memory, but its destructive electrical reading step requires a rewrite step after each reading, increasing energy consumption. As an alternative, optical nondestructive readout is based on the ferroelectric polarization dependence of the photovoltaic response in materials and has been reported in two-states ferroelectric memories and multistate devices with limited photocurrent switchability due to asymmetric interfacial effects. In this work, we report a nonvolatile oxide memory device based on a symmetric heterostructure with eight stable and well-controlled remanent polarization (Pr) states, written electrically by voltage pulse and read optically through polarization-dependent short-circuit photocurrent Isc or open circuit photovoltage Voc. This symmetric capacitor demonstrates a clear proportionality between Isc (Voc) and Pr, allowing to achieve a 100% switchability of the photovoltaic response. The memory devices based on 3-bit data storage show good performance in terms of data retention, fatigue behavior, and repeatability of writing and reading cycles. Thanks to the very high sensitivity of the optical reading method, the number of states could largely exceed eight, being limited only by the electrical writing step precision. These results are particularly exciting for the development of next-generation ferroelectric memory devices with increased memory storage density and lower power consumption.