And in that case, there's a nice complete list available as a link from that page, so you can just do it by table lookups.

#!/usr/bin/perl -w

# Silly super-efficient interactive narcissistic checker...

use strict;

# http://mathworld.wolfram.com/packages/Narcissistic.dat
my %narcs=map {$_ => 1} (
0,1,2,3,4,5,6,7,8,9,153,370,371,407,1634,8208,9474,54748,92727,93084,
548834,1741725,4210818,9800817,9926315,24678050,24678051,88593477,
146511208,472335975,534494836,912985153,4679307774,32164049650,
32164049651,40028394225,42678290603,44708635679,49388550606,
82693916578,94204591914,28116440335967,4338281769391370,
4338281769391371,21897142587612075,35641594208964132,35875699062250035
+,
1517841543307505039,3289582984443187032,4498128791164624869,
4929273885928088826,63105425988599693916,128468643043731391252,
449177399146038697307,21887696841122916288858,27879694893054074471405,
27907865009977052567814,28361281321319229463398,
35452590104031691935943,174088005938065293023722,
188451485447897896036875,239313664430041569350093,
1550475334214501539088894,1553242162893771850669378,
3706907995955475988644380,3706907995955475988644381,
4422095118095899619457938,121204998563613372405438066,
121270696006801314328439376,128851796696487777842012787,
174650464499531377631639254,177265453171792792366489765,
14607640612971980372614873089,19008174136254279995012734740,
19008174136254279995012734741,23866716435523975980390369295,
1145037275765491025924292050346,1927890457142960697580636236639,
2309092682616190307509695338915,17333509997782249308725103962772,
186709961001538790100634132976990,186709961001538790100634132976991,
1122763285329372541592822900204593,12639369517103790328947807201478392
+,
12679937780272278566303885594196922,
1219167219625434121569735803609966019,
12815792078366059955099770545296129367,
115132219018763992565095597973971522400,
115132219018763992565095597973971522401);

while(<>) {
    chomp;
    if(exists $narcs{$_}) {
        print "Is narc, dude\n";
    }
    else {
        print "Not narc, please try again\n";
    }
}
[download]

But if it's really numbers equal to the sum of their digits ** 3, then I'm not sure what the exhaustive list would look like...

I think there WOULD be one, though, since 9**3 is only 729, so that limits how big your number could be. So you could still precompute the possible answers, if you needed an efficient way to answer this question...

Hehe, it doesn't seem to be a problem that cries out for optimization, does it? :)
--
Mike