Rust のパッケージは Cargo.toml で管理されていますが，npm のように install コマンドで全てのパッケージが簡単に更新できるような感じではないようです．

Update packages individually

Update to the latest version

$ cargo update -p PACKAGE

It seems that it is also available for install command.

$ cargo install -f PACKAGE

Update to the specific version

$ cargo update -p PACKAGE --precise x.x.x

Update packages in bulk

There is a tool called cargo-update that updates packages in bulk.

$ cargo install cargo-update
$ cargo install-update -a

When executed, all packages are updated to the latest version possible without breaking dependencies.

Error

The following error may occur when using the install command.

Reference: cargo install - The Cargo Book

If the package does not have an executable file, the install command does not seem to work. In this case, you need to edit the Cargo.toml file.

You can check the version of the package you want to install and its dependencies at crates.io. After editing the Cargo.toml, a cargo build will fetch the package and update the Cargo.lock.