From the App Store download Mailbox and Dropbox apps for iPhone (as shown in steps 1 and 2)
Download the Mailbox app by Orchestra Inc which is now acquired by Dropbox!
Download the one of the most famous cloud storage services app; Dropbox!
Login to both apps, Mailbox with your Gmail account, and to Dropbox app with your Dropbox account!
Link your Mailbox account to Dropbox account, from inside the Mailbox app.
Click the More icon on the top left corner to link your accounts together!
Tap on Setting!
Tap the Dropbox option!
Tap the Add Dropbox Account! Fill your login information if asked
Allow the Mailbox to access your Dropbox folders
Now we'll send an email with an attachment!
Now tap the Compose icon on the right top corner!
Then tap the Attach icon (above the keyboard, next to the Camera icon)
Browse to the folder where the attachment exists
And you're done! All file types can be attached!