Вам нужно также сделать Second
группой.
@bot.group(pass_context=True)
async def First(ctx):
if ctx.invoked_subcommand is None:
await bot.say('Invalid sub command passed...')
@First.group(pass_context=True)
async def Second(ctx):
if ctx.invoked_subcommand is Second:
await bot.say('Invalid sub command passed...')
@Second.command(pass_context=True)
async def Third(ctx):
msg = 'Finally got success {0.author.mention}'.format(ctx.message)
await bot.say(msg)