Forecasting the amplitude and timing of the sunspot cycle is highly important for solar physics and space weather applications, but high-precision prediction of solar magnetic activity has remained an outstanding challenge. The Informer model, as the most advanced deep learning technique, is an ideal approach for predicting solar activity cycle. Using the whole-disk sunspot numbers (SSNs) between 1749 and 2023 and the hemispheric SSNs between 1992 and 2023, the amplitudes and timings of Solar Cycles 25 and 26 are predicted by the Informer model. The main results are the following: (1) the activity levels of Solar Cycles 25 and 26 continue being weak-moderate cycles with their strengths stronger than Solar Cycle 24, implying that the long-term solar variability is significantly modulated in length and magnitude by the Gleissberg century cycle; (2) the Gnevyshev peaks of Solar Cycles 25 and 26 are clearly observed with a higher value in the second peak, suggesting that the numbers of the large sunspot groups are greater compared to the small sunspot groups in these two cycles; and (3) during Solar Cycle 25, the activity level in the southern hemisphere is predicted to be stronger than that in the northern one, revealing significant asymmetry and asynchronization between the two hemispheres. Our analysis results show that solar cycle predictions can be made more accurate if performed separately for each hemisphere. Furthermore, Solar Cycles 25 and 26 are likely to be weak-moderate cycles, in agreement with the precursor-based and model-based prediction methods.