Metastatic prostate cancer to the bone: This is the most likely diagnosis given the history of prostate cancer. Prostate cancer commonly metastasizes to the bones, particularly the spine, pelvis, and ribs, causing back pain.

Degenerative disc disease or spinal stenosis: These are common causes of back pain in older adults and can be exacerbated by the decreased mobility and bone density changes associated with prostate cancer treatment.
Musculoskeletal strain: Back pain can also result from musculoskeletal strain due to decreased mobility, altered posture, or overuse, which can be more common in patients with a history of cancer.
Osteoporotic compression fracture: Patients with prostate cancer, especially those on androgen deprivation therapy, are at increased risk of osteoporosis, which can lead to compression fractures and back pain.

Spinal cord compression: This is a medical emergency that can occur when a metastatic lesion compresses the spinal cord, leading to neurological deficits. Prompt diagnosis and treatment are crucial to prevent permanent damage.
Infection (e.g., osteomyelitis, discitis): Infections of the spine can cause severe back pain and are more common in immunocompromised patients, such as those undergoing cancer treatment.
Pathological fracture: A fracture that occurs in a bone weakened by metastatic disease can cause sudden and severe back pain.

Multiple myeloma: Although less common, multiple myeloma is another type of cancer that can cause back pain due to bone lesions and should be considered in the differential diagnosis, especially if there are other suggestive symptoms or lab findings.
Paget's disease of the bone: This rare condition can cause bone pain, including back pain, due to abnormal bone remodeling and should be considered if other causes are ruled out.