Adrenocortical Carcinoma: This is the most likely diagnosis due to the presence of a large adenoma, low ACTH levels (indicating possible autonomous cortisol production), and increased DHEAs (a marker often elevated in adrenocortical carcinomas). The size of the adenoma and the hormonal profile suggest a malignant potential.

Functioning Adrenal Adenoma: Although less likely than carcinoma given the size and hormonal profile, a large functioning adrenal adenoma could produce similar clinical and biochemical findings, including low ACTH and elevated DHEAs, due to autonomous cortisol production.
Congenital Adrenal Hyperplasia (CAH): Certain forms of CAH can lead to adrenal hyperplasia and increased production of androgens like DHEAs. However, the presence of a large adenoma would be unusual in this context.

Pheochromocytoma: Although pheochromocytomas primarily produce catecholamines, some can co-secrete other hormones, and their diagnosis is critical due to the potential for severe hypertension and cardiovascular complications. The presence of a large adrenal mass necessitates ruling out pheochromocytoma.
Metastasis to the Adrenal Gland: Given the size of the adenoma, it's crucial to consider the possibility of metastasis from another primary cancer, especially in patients with a known history of cancer. This diagnosis would significantly alter management and prognosis.

Primary Pigmented Nodular Adrenal Disease (PPNAD): A rare cause of Cushing's syndrome characterized by multiple small nodules in the adrenal glands. It's less likely given the description of a large adenoma but could be considered in the differential diagnosis of adrenal disorders with abnormal hormone production.
Familial Adrenocortical Carcinoma: Part of the Li-Fraumeni syndrome, this is a rare hereditary condition that increases the risk of developing adrenocortical carcinoma among other cancers. The diagnosis would be considered in the context of a family history of similar cancers.