Diabetic Ketoacidosis (DKA): This condition is characterized by hyperglycemia, metabolic acidosis, and increased levels of ketone bodies. The elevated BUN (Blood Urea Nitrogen) can be seen due to dehydration, a common feature in DKA, which concentrates the blood and thus increases BUN levels.

Dehydration: Dehydration can cause an increase in BUN due to decreased renal perfusion and concentrated blood. Hyperglycemia can also be present if the dehydration is due to uncontrolled diabetes or if the patient has been unable to keep up with fluid intake due to another illness.
Sepsis: Sepsis can lead to acute kidney injury, which may result in an elevated BUN. Hyperglycemia is also common in sepsis due to the stress response and potential insulin resistance.
Acute Kidney Injury (AKI): AKI can cause an elevation in BUN due to decreased renal function. Hyperglycemia may be present if the patient has diabetes or if the AKI is caused by a condition that also affects glucose metabolism.

Urosepsis: Although less common, urosepsis (a severe infection of the urinary tract) can lead to AKI, resulting in elevated BUN, and can also cause hyperglycemia due to the systemic inflammatory response.
Hyperosmolar Hyperglycemic State (HHS): Similar to DKA but without significant ketosis, HHS can present with very high glucose levels and elevated BUN due to severe dehydration.

Rhabdomyolysis: This condition involves the breakdown of muscle tissue, which can lead to AKI and thus an elevated BUN. Hyperglycemia may be present due to the stress response or underlying conditions.
Adrenal Insufficiency: Although rare, adrenal insufficiency can lead to hyperglycemia and, in severe cases, acute kidney injury, resulting in an elevated BUN.