This research experimentally investigates the mechanical behavior of innovative sandwich panels with expanded cork agglomerate cores under quasi-static indentation and three-point bending tests. Two types of cork cores, including dry cork (SPDC3) and cork with rubber particles (SPC3), were used in a monolithic configuration, while a layered core configuration (LSPC1) consisting of alternating layers of cork with rubber particles and glass fiber/epoxy composite was also examined. The face sheets of all sandwich panels were made of glass fiber/epoxy composite with a 0/90 layup. A reference specimen, an 8-layer glass fiber/epoxy composite plate (GE8), was also tested for comparison. The indentation test results showed that the SPDC3 sample exhibited the highest energy absorption due to the core crushing mechanism, whereas the presence of rubber particles had a negative effect on both indentation resistance and energy absorption under quasi-static loading. In the bending test, the GE8 sample demonstrated the highest flexural strength but failed in a brittle manner. In contrast, the SPDC3 sample, despite having lower flexural strength than GE8, exhibited significantly higher energy absorption (16.5 J compared to 9.43 J) due to the core crushing mechanism. The LSPC1 sample, while having lower flexural strength than SPDC3, showed the highest ultimate displacement (31.9 mm) and recovered to its original shape after unloading, indicating a unique ductility. Damage analysis revealed different failure mechanisms, including brittle fiber failure in GE8, delamination in LSPC1, and core crushing in SPDC3 and SPC3. Although the reference sample (GE8) showed higher flexural strength, the sandwich panels with expanded cork agglomerate cores, especially those with dry cork, demonstrated considerable potential in applications requiring high energy absorption and a more ductile behavior under quasi-static loading, highlighting the high potential of these novel materials as a suitable alternative to traditional structures.