Jelly, 16 30 29 20 bytes

Now with the correct output format! Many thanks to Dennis for his help in debugging this answer. Golfing suggestions welcome. Try it online!

Edit: +14 bytes from using the correct output format. -1 byte from removing an extra space. -3 from changing from 24,60,60 to “ð<<‘. -6 bytes from changing +100DḊ€€ to d⁵.

“ð<<‘Œp’S=¥Ðfd⁵j€”:Y

Explanation

“ð<<‘Œp’S=¥Ðfd⁵j€”:Y  Main link. Argument: n

“ð<<‘                 Jelly ord() the string `ð<<` to get [24, 60, 60]. Call this list z.
     Œp               Cartesian product of z's items. 
                        Since each item of z is a literal,
                        Jelly takes the range [1 ... item] for each item.
       ’              Decrements every number in the Cartesian product 
                        to get lowered ranges [0 ... item-1].
        S=¥           Create a dyadic link of `sum is equal to (implicit n)`.
           Ðf         Filter the Cartesian product for items with sum equal to n.
             d⁵       By taking divmod 10 of every number in each item,
                        we get zero padding for single-digit numbers
                        and every double-digit number just turns into a list of its digits.
               j€”:   Join every number with a ':'.
                   Y  Join all of the times with linefeeds for easier reading.

Bash, 71

• 8 bytes saved thanks to @hvd

for t in {0..23}+{00..59}+{00..59};{((${t//+0/+}-$1))||echo ${t//+/:};}

Try it online.

Python 3, 91 bytes

def f(n):
 for k in range(86400):t=k//3600,k//60%60,k%60;sum(t)==n!=print('%d:%02d:%02d'%t)

There are shorter solutions using exec (Python 2) or recursion (Python 3), but both require an unreasonable amount of memory.

Try it online!

PowerShell, 87 77 bytes

Saved 10 bytes thanks to John L. Bevan

$d=date;0..86399|%{$d+=1e7l;"$d".Split()[1]}|?{("{0:H+m+s}"-f$d|iex)-in$args}

Try it online! (this will time out, it's very slow)

Explanation

Pretty simple, starting with the current [datetime], add 1 second 86,399 times, format as a string, then keep only the ones where sum adds up.

Haskell, 77 bytes

f x=[tail$(':':).tail.show.(+100)=<<t|t<-mapM(\x->[0..x])[23,59,59],sum t==x]

Pyth - 30 bytes

Takes all possible times then filters.

mj\:%L"%02d"dfqsTQsM*U24*KU60K

Test Suite.

Perl 6, 62 56 bytes

{map *.fmt('%02d',':'),grep $_==*.sum,(^24 X ^60 X ^60)}

Just checks all possible combinations in the cross product of all hours, minutes, and seconds.

Haskell, 90 bytes

p x=['0'|x<10]++show x
i=[0..59]
f x=[p h++':':p m++':':p s|h<-[0..23],m<-i,s<-i,h+m+s==x]

Returns a list of HH:MM:SS strings, e.g. f 140 -> ["22:59:59","23:58:59","23:59:58"].

It's three simple loops through the hours, minutes and seconds. Keep and format all values where the sum is the input number x.

Octave, 83 , 87 bytes

@(a){[H,M,S]=ndgrid(0:23,s=0:59,s);printf("%d:%02d:%02d\n",[H(x=H+M+S==a),M(x),S(x)]')}

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Julia 0.5, 69 bytes

!n=[h+m+s==n&&@printf("%d:%02d:%02d
",h,m,s)for s=0:59,m=0:59,h=0:23]

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Batch, 168 bytes

@for /l %%t in (0,1,86399)do @call:c %1 %%t
@exit/b
:c
@set/ah=%2/3600,m=%2/60%%60,s=%2%%60,n=%1-h-m-s
@set m=0%m%
@set s=0%s%
@if %n%==0 echo %h%:%m:~-2%:%s:~-2%

Outputs single-digit hours.

Mathematica, 79 bytes

Cases[Tuples@{(r=Range)@24-1,x=r@60-1,x},t_/;Tr@t==#:>DateString@TimeObject@t]&

JavaScript, 120 118 bytes

Takes one additional empty string as input, which I presume doesn't count towards the size.

console.log((
//Submission starts at the next line
i=>o=>{for(h=24;h--;)for(m=60;m--;)for(s=60;s--;)if(h+m+s==i)o+=`${h}:0${m}:0${s} `;return o.replace(/0\d{2}/g,d=>+d)}
//End submission
)(prompt("Number:",""))(""))

QBIC, 82 72 bytes

:[0,23|[0,59|[0,59|~b+c+d=a|?!b$+@:`+right$(@0`+!c$,2)+A+right$(B+!d$,2)

This hits an unfortunate spot in QBasic, with casting to number, trimming and prepending a 0 when necessary is really costly.

Sample output:

Command line: 119
1:59:59
2:58:59
2:59:58
3:57:59
[... SNIP 270 lines ...]
23:58:38
23:59:37

Explanation I wrote a novel about it:

:           Get N, call it 'a'
[0,23|      Loop through the hours; this FOR loop is initialised with 2 parameters
            using a comma to separate FROM and TO, and a '|' to delimit the argument list
[0,59|      Same for the minutes
[0,59|      And the seconds
            QBIC automatically creates variables to use as loop-counters: 
            b, c, d (a was already taken by ':')
~b+c+d=a    IF a == b+c+d
|           THEN
 ?          PRINT
  !         CAST
   b        'b'
    $       To String; casting num to str in QBasic adds a space, this is trimmed in QBIC
+@:`        Create string A$, containing ":"
+right$      This is a QBasic function, but since it's all lowercase (and '$' is 
            not a function in QBIC) it remains unaltered in the resulting QBasic.
(@0`+!c$,2) Pad the minutes by prepending a 0, then taking the rightmost 2 characters.
+A          Remember that semicolon in A$? Add it again
+right$     Same for the seconds
(B+!d$,2)   Reusing the 0-string saves 2 bytes :-)

Racket 39 bytes

(for*/sum((h 24)(m 60)(s 60))(+ h m s))

Ungolfed:

(for*/sum      ; loop for all combinations; return sum of values for each loop
   ((h 24)     ; h from 0 to 23
    (m 60)     ; m from 0 to 59
    (s 60))    ; s from 0 to 59
  (+ h m s))   ; sum of all 3 variables

MATL, 29 bytes

24:q60:qt&Z*t!si=Y)'%i:'8:)&V

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Explanation

24:q     % Push [0 1 ... 23]
60:q     % Push [0 1 ... 59]
t        % Duplicate
&Z*      % Cartesian product of the three arrays. This gives a matrix with each
         % on a different row Cartesian tuple
t!       % Push a transposed copy
s        % Sum of each column
i=       % Logical mask of values that equal the input
Y)       % Select rows based on that mask
'%i:'    % Push this string
8:)      % Index (modularly) with [1 2 ... 8]: gives string '%i:%i:%i'
&V       % Convert to string with that format specification. Implicitly display

[PowerShell], 91 97 bytes (including input)

param($x)1..864e3|%{($d=date($_*1e7l))}|?{("{0:H+m+s}"-f$_|iex)-eq$x}|%{"{0:H:mm:ss}"-f$_}

param($x)0..23|%{$h=$_;0..59|%{$m=$_;0..59|?{$h+$m+$_-eq$x}|%{"{0:0}:{1:00}:{2:00}"-f$h,$m,$_}}}

or

param($x)0..23|%{$h=$_;0..59|?{($s=$x-$h-$_)-le59-and$s-ge0}|%{"{0:0}:{1:00}:{2:00}"-f$h,$_,$s}} <\s>

Expanded & commented

param($x)
#loop through the hours
0..23 | %{
    $h=$_
    #loop through the minutes
    0..59 | %{
        $m=$_
        #loop through the seconds
        0..59 | ?{ #filter for those where the sum matches the target
            $h + $m + $_ -eq $x
        } | %{
            #format the result
            "{0:#0}:{1:00}:{2:00}" -f $h, $m, $_
        }
    }
}

[PowerShell], 79 Bytes (nasty version)

Since the rules say nothing about completing in a certain time (or at all), and nothing about no duplicates, here's a horrific solution:

param($x)for(){if(($d=Date).Second+$d.Minute+$d.Hour-eq$x){"{0:H:mm:ss}"-f$d}}