Do this:
M-x octave mode

Observe this error message:
Cannot open load file: no such file or directory, octave-mod

Author says these files should be installed:
https://www.gnu.org/software/octave/doc/interpreter/Installing-EOS.html#Installing-EOS

But they are not.

Looks like the file got renamed.

Here's how I fixed it:

$cd /usr/local/Cellar/emacs/24.5/share/emacs/24.5/lisp/progmodes
$mv octave.el.gz octave-mod.el.gz
$mv octave.elc octave-mod.elc

I didn't see the authors other 2 files in distribution though.
octave-inf.el, octave-hlp.el

C-h a mode
...
519 octave-mode                   M-x ... RET
520    (not documented)




In GNU Emacs 24.5.1 (x86_64-apple-darwin14.3.0, NS apple-appkit-1347.57)
 of 2015-05-19 on Alexs-MacBook-Pro-2.local
Configured using:
 `configure --prefix=/usr/local/Cellar/emacs/24.5
 --enable-locallisppath=/usr/local/share/emacs/site-lisp
 --infodir=/usr/local/Cellar/emacs/24.5/share/info/emacs --without-dbus
 --without-gnutls --with-ns --disable-ns-self-contained'

Important settings:
  value of $LANG: en_US.UTF-8
  locale-coding-system: utf-8-unix

Major mode: Octave

Minor modes in effect:
  global-linum-mode: t
  linum-mode: t
  tooltip-mode: t
  electric-indent-mode: t
  mouse-wheel-mode: t
  tool-bar-mode: t
  menu-bar-mode: t
  file-name-shadow-mode: t
  global-font-lock-mode: t
  font-lock-mode: t
  auto-composition-mode: t
  auto-encryption-mode: t
  auto-compression-mode: t
  line-number-mode: t
  transient-mark-mode: t

Recent messages:
File mode specification error: (file-error "Cannot open load file" "no such
file or directory" "octave-mod")
End of buffer [2 times]
Auto-saving...
command-execute: Cannot open load file: no such file or directory,
octave-mod
Type C-x 4 C-o RET to restore the other window.
Mark saved where search started
Type "q" to restore previous buffer, M-x scroll-up to scroll help.
Making completion list... [2 times]
command-execute: Cannot open load file: no such file or directory,
octave-mod
Auto-saving...done

Load-path shadows:
None found.

Features:
(shadow sort gnus-util mail-extr emacsbug message format-spec rfc822 mml
mml-sec mm-decode mm-bodies mm-encode mail-parse rfc2231 mailabbrev
gmm-utils mailheader sendmail rfc2047 rfc2045 ietf-drums mm-util
mail-prsvr mail-utils octave smie comint ansi-color ring pp help-fns
misearch multi-isearch apropos help-mode easymenu xterm time-date linum
tooltip electric uniquify ediff-hook vc-hooks lisp-float-type mwheel
ns-win tool-bar dnd fontset image regexp-opt fringe tabulated-list
newcomment lisp-mode prog-mode register page menu-bar rfn-eshadow timer
select scroll-bar mouse jit-lock font-lock syntax facemenu font-core
frame cham georgian utf-8-lang misc-lang vietnamese tibetan thai
tai-viet lao korean japanese hebrew greek romanian slovak czech european
ethiopic indian cyrillic chinese case-table epa-hook jka-cmpr-hook help
simple abbrev minibuffer nadvice loaddefs button faces cus-face macroexp
files text-properties overlay sha1 md5 base64 format env code-pages mule
custom widget hashtable-print-readable backquote make-network-process
cocoa ns multi-tty emacs)

Memory information:
((conses 16 97306 5730)
 (symbols 48 18153 0)
 (miscs 40 482 228)
 (strings 32 12463 4587)
 (string-bytes 1 335911)
 (vectors 16 8319)
 (vector-slots 8 347347 22744)
 (floats 8 63 697)
 (intervals 56 4453 57)
 (buffers 960 17))