Hardy's Taxicab -- c'mon, you can do this

Okay, now I ain't no Ramanujan, that's for sure.

But I just solved the problem of Hardy's Taxicab number.

Okay, so I didn't solve it in my head while lying in bed.

And I didn't solve it with algebra, pencil and paper.

I used the computer. I programmed the computer to Brute-Force the sucker. I used a programming language that's so primitive I'm embarrassed to tell you its name.

Took me about 10 minutes to program it. Then when I ran it, it spat the answer back in about 1 second.

This is hardly a Life Commitment to Higher Mathematics.

But no matter how you do it, everybody will say, "Wow! He/She's Smart!"

You can do this. Trust me.

Hardy wrote:

I remember once going to see [Ramanujan] when he was lying ill at Putney. I had ridden in taxi cab number **** and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen.

"No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."

Vleeptron PizzaQ Honor Code -- no Googling, etc., just pure, solitary brainwork. (Oh, okay, you can program your computer to find the answer -- but remember that Ramanujan got the answer just lying in a hospital bed.)

What was the number of Hardy's taxicab?