How to execute sqlcmd from powershell?

You could also stop using the external 'SQLCMD.EXE' and use the Invoke-Sqlcmd cmdlet instead:

Invoke-Sqlcmd is a SQL Server cmdlet that runs scripts that contain statements from the languages (Transact-SQL and XQuery) and commands that are supported by the sqlcmd utility

Just open the 'sqlps' utility and run

Invoke-Sqlcmd -InputFile "C:\temp\sql.sql"

Please see Running SQL Server PowerShell

You can also load the SQL Server snap-ins manually in PowerShell before using 'Invoke-Sqlcmd';
for MS SQL Server 2012 you can do that by running
Import-Module SqlPs

To call a Win32 executable you want to use the call operator & like this:

& sqlcmd -S "(local)\instance1" -U a -P a -i "c:\temp\sql.sql"