What is the best route to get to Cuba from India?
In airways. Cheap and quick. And has a balance between those two.
For the quickest, you either want a direct flight, or a change at an airport on the great circle path.
I can't seem to find an Indian airlines serving Havana directly, so that's the first option out. For the 2nd option, the great circle path goes over Scandinavia. So, for that, your best bet would be to change there.
Unfortunately, according to the wikipedia list of airlines serving Havana, I don't think that any of the Scandinavian airlines go there.
Next best would be the UK - it's not far off the great circle path. Virgin Atlantic fly to Havana from London Gatwick, and they also fly to a number of airports in India. Assuming the connection times in London work from your home airport, that'll be the quickest. Not sure if it's the cheapest though (I searched for some random dates about 2 months into the future, and the price was around the INR40,000 mark for a return, which seems a little high). There are a number of UK based charter airlines that serve Cuba, who are often quite cheap, especially if you book accommodation with them. It may be worth checking if a return to the UK on any of the airlines that serve the UK from India, followed by changing airlines onto a charter flight to Cuba will be cheaper, as I suspect it will be. Disadvantage of this is you'll need to exit airside to re-check your bags, and that will probably need a different kind of visa...
In addition to going via the UK, Air France serve quite a few Indian cities, and fly to Cuba from Paris, and aren't that much further off the great circle. Some thing for KLM from Amsterdam.