KeepVid Pro lets you download files to your iPhone, iPad.
KeepVid Pro includes a music player to let you play offline files.
KeepVid Pro supports for Dropbox, Box, Google Drive, OneDrive, and many more to come such as Web Browser.

Highlights >
Download files to local for offline use
Powerful playlist manager for audio, video files
Audio video player with background playback and lock screen controls

Features >
Switch account if you have more than one
Search for files by name and content
Share files and folders easily with others
Transfer files from one account to another account
Upload photos, videos from library to cloud
Move files around within an account
Rename, delete, copy files
View documents, PDFs, photos, videos and more

Disclaimer >
This app does not provide content. By conforming to each Dropbox, Box, Google Drive, OneDrive API Terms of Service, this app allows users to manage their files.
The download feature is allowed by Dropbox, Box, Google Drive, OneDrive API. For more information, see the guideline of each cloud drive as below.
Dropbox > https://www.dropbox.com/developers/documentation/http/documentation#files-download
Box > https://docs.box.com/reference#download-a-file
Google Drive > https://developers.google.com/drive/v3/web/manage-downloads
OneDrive > https://dev.onedrive.com/items/download.htm