Python 2, 135 122 bytes

• Quite long since this includes all the procedures: prime-check, obtain-prime factors and check sphere number condition.

lambda x:(lambda t:len(t)==3and t[0]*t[1]*t[2]==x)([i for i in range(2,x)if x%i<1and i>1and all(i%j for j in range(2,i))]) 

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Python 2, 135 121 bytes

• Quite long since this includes all the procedures: prime-check, obtain-prime factors and check sphere number condition.

lambda x:(lambda t:len(t)>2and t[0]*t[1]*t[2]==x)([i for i in range(2,x)if x%i<1and i>1and all(i%j for j in range(2,i))]) 

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Python 2, 135 bytes

• Quite long since this includes all the procedures: prime-check, obtain-prime factors and check sphere number condition.

lambda x:(lambda t:len(t)==3and t[0]*t[1]*t[2]==x)([i for i in range(2,x)if x%i<1and(lambda x:x>1and all(x%i for i in range(2,x)))(i)]) 

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Python 2, 135 122 bytes

• Quite long since this includes all the procedures: prime-check, obtain-prime factors and check sphere number condition.

lambda x:(lambda t:len(t)==3and t[0]*t[1]*t[2]==x)([i for i in range(2,x)if x%i<1and i>1and all(i%j for j in range(2,i))]) 

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Python 2, 140 bytes

lambda x:(lambda t,x:len(t)==3 and t[0]*t[1]*t[2]==x)([i for i in range(2,x)if x%i<1and(lambda x:x>1and all(x%i for i in range(2,x)))(i)],x) 

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Python 2, 135 bytes

• Quite long since this includes all the procedures: prime-check, obtain-prime factors and check sphere number condition.

lambda x:(lambda t:len(t)==3and t[0]*t[1]*t[2]==x)([i for i in range(2,x)if x%i<1and(lambda x:x>1and all(x%i for i in range(2,x)))(i)]) 

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