cargo build-bpf
BPF SDK: /opt/solana-release/bin/sdk/bpf
thread 'main' panicked at 'Failed to install bpf-tools: "Permission denied (os error 13)"', sdk/cargo-build-bpf/src/main.rs:440:6
note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace
It sounds like the script is trying to install bpf-tools globally and your current user doesn't have adequate permissions.
Does the cargo-build-bpf project provide instructions for how to install them yourself? Otherwise, you can probably just run sudo cargo build-bpf to give it adequate permissions, although I'm always wary of running unknown/untrusted programs as root on my development machine.
The error message said it couldn't install "bpf-tools", not "cargo-bpf".
The error message mentioned solana, and after searching their issue tracker on GitHub for "bpf-tools" it looks like this issue has already been reported.
The solution is to run cargo build-bpf as root so it can create the appropriate symlink.