If the mailbox was purchased for (and exclusively used by) the business, then you can deduct the cost of the box and the post.
"Mail service" is an ordinary and necessary expense in conducting most businesses.
From the IRS What Can I Deduct?: To be deductible, a business expense must be both ordinary and necessary. An ordinary expense is one that is common and accepted in your trade or business. A necessary expense is one that is helpful and appropriate for your trade or business. An expense does not have to be indispensable to be considered necessary.
