What causes extreme buttock pain with radiating pain down entire leg?

Pyriformis v disc. This sounds like sciatica(pain over this large leg nerve's distribution to the foot from the buttock) which can occur due to a disc herniation in the lower back compressing a spinal nerve and not cause any back pain or be due to a hip muscle known as the pyriformis irritating the sciatic nerve which it straddles in the buttock region mimicking a disc herniation pattern.
A pinched nerve. A pinched nerve or compressed nerve root (sciatica) can cause pain in the buttock going down the leg in the distribution of the nerve which is compressed. The most common causes of pinched nerves are herniated discs and bony spurs.

Related Questions

How can you suddenly get extreme buttock pain with radiating pain down entire leg?

Varies. Usually sudden pain from the buttocks to the leg is associated with "sciatica", often due to disc herniation. There are other causes such as nerve compression from spinal instability, sacroiliac dysfunction, pyriformis syndrome, and even osteoporotic fractures to the sacrum. If severe, and if having weakness, loss of sensation, and/or bowel/bladder issues, seek out emergency evaluation. Read more...