Task: Taxicab numbers
C++: #include <algorithm>
#include <iomanip>
#include <iostream>
#include <map>
#include <sstream>
#include <vector>

template <typename T>
size_t indexOf(const std::vector<T> &v, const T &k) {
    auto it = std::find(v.cbegin(), v.cend(), k);

    if (it != v.cend()) {
        return it - v.cbegin();
    }
    return -1;
}

int main() {
    std::vector<size_t> cubes;

    auto dump = [&cubes](const std::string &title, const std::map<int, size_t> &items) {
        std::cout << title;
        for (auto &item : items) {
            std::cout << "\n" << std::setw(4) << item.first << " " << std::setw(10) << item.second;
            for (auto x : cubes) {
                auto y = item.second - x;
                if (y < x) {
                    break;
                }
                if (std::count(cubes.begin(), cubes.end(), y)) {
                    std::cout << " = " << std::setw(4) << indexOf(cubes, y) << "^3 + " << std::setw(3) << indexOf(cubes, x) << "^3";
                }
            }
        }
    };

    std::vector<size_t> sums;

    
    for (size_t i = 0; i < 1190; i++) {
        auto cube = i * i * i;
        cubes.push_back(cube);
        for (auto j : cubes) {
            sums.push_back(cube + j);
        }
    }
    std::sort(sums.begin(), sums.end());

    
    auto nm1 = sums[0];
    auto n = sums[1];
    int idx = 0;
    std::map<int, size_t> task;
    std::map<int, size_t> trips;

    auto it = sums.cbegin();
    auto end = sums.cend();
    it++;
    it++;

    while (it != end) {
        auto np1 = *it;

        if (nm1 == np1) {
            trips.emplace(idx, n);
        }
        if (nm1 != n && n == np1) {
            if (++idx <= 25 || idx >= 2000 == idx <= 2006) {
                task.emplace(idx, n);
            }
        }
        nm1 = n;
        n = np1;

        it++;
    }

    dump("First 25 Taxicab Numbers, the 2000th, plus the next half-dozen:", task);

    std::stringstream ss;
    ss << "\n\nFound " << trips.size() << " triple Taxicabs under 2007:";
    dump(ss.str(), trips);

    return 0;
}

Java: import java.util.PriorityQueue;
import java.util.ArrayList;
import java.util.List;
import java.util.Iterator;

class CubeSum implements Comparable<CubeSum> {
	public long x, y, value;

	public CubeSum(long x, long y) {
		this.x = x;
		this.y = y;
		this.value = x*x*x + y*y*y;
	}

	public String toString() {
		return String.format("%4d^3 + %4d^3", x, y);
	}

	public int compareTo(CubeSum that) {
		return value < that.value ? -1 : value > that.value ? 1 : 0;
	}
}

class SumIterator implements Iterator<CubeSum> {
	PriorityQueue<CubeSum> pq = new PriorityQueue<CubeSum>();
	long n = 0;

	public boolean hasNext() { return true; }
	public CubeSum next() {
		while (pq.size() == 0 || pq.peek().value >= n*n*n)
			pq.add(new CubeSum(++n, 1));

		CubeSum s = pq.remove();
		if (s.x > s.y + 1) pq.add(new CubeSum(s.x, s.y+1));

		return s;
	}
}

class TaxiIterator implements Iterator<List<CubeSum>> {
	Iterator<CubeSum> sumIterator = new SumIterator();
	CubeSum last = sumIterator.next();

	public boolean hasNext() { return true; }
	public List<CubeSum> next() {
		CubeSum s;
		List<CubeSum> train = new ArrayList<CubeSum>();

		while ((s = sumIterator.next()).value != last.value)
			last = s;

		train.add(last);

		do { train.add(s); } while ((s = sumIterator.next()).value == last.value);
		last = s;

		return train;
	}
}
	
public class Taxi {
	public static final void main(String[] args) {
		Iterator<List<CubeSum>> taxi = new TaxiIterator();

		for (int i = 1; i <= 2006; i++) {
			List<CubeSum> t = taxi.next();
			if (i > 25 && i < 2000) continue;

			System.out.printf("%4d: %10d", i, t.get(0).value);
			for (CubeSum s: t)
				System.out.print(" = " + s);
			System.out.println();
		}
	}
}