With begomoas, the blooms depend on the amount of sun rather that length of time from taking the cutting.
I have had cuttings rooting in a jar bloom.
Also, what kind of begonias are they?
Linda C

Thanks for your reply. I don't know the type name. I am giving link of a photo which looks similar to my begonia.

currently they are in a place where they get only morning sun. I will move them to more sunny place today.

Here is a link that might be useful: {{gwi:22890}}

Those are just your standard bedding type fibrous begonias and they bloom reliably through the winter. Some other types of begonias bloom only during specific light levels (as winter blooming vs. summer blooming) but the fibrous can bloom all year. They want ample indirect light in a house situation, or lamps.

Their botanical name (Begonia semperflorens-cultorum) gives us a clue about their flowering habits. 'Semperflorens' means 'ever blooming'. In my experience, cuttings will begin to regrow flower buds even before the new roots begin to develop right there in their rooting flats!

Perhaps you need to review your cultural program for these predictable tender perennials?